Medical Tests Medical Tests Certifications MCAT-TEST Questions & Answers

• Question 331:

  Aski jump is an inclined track from which a ski jumper takes off through the air. After traveling down the track, the skier takes off from a ramp at the bottom of the track. The skier lands farther down on the slope.

  Figure 1 shows a ski jump, in which the ramp at the lower end of the track makes an angle of 30° to the horizontal. The track is inclined at an angle of to the horizontal and the slope is inclined at an angle of 45° to the horizontal. A ski jumper is stationary at the top of the track. Once the skier pushes off, she accelerates down the track, and then takes off from the ramp. The vertical height difference between the top of the track and its lowest point is 50 m, and the vertical height difference between the top of the ramp and its lowest point is 10 m.

  

  Figure 1

  The distance traveled by the skier between leaving the ski jump ramp and making contact with the slope is called the jump distance. In some cases, in order to increase the jump distance a skier will jump slightly upon leaving the ramp,

  thereby increasing the vertical velocity. Unless otherwise stated, assume that friction between the skis and the slope is negligible, and ignore the effects of air resistance.

  How would the work done by gravity on the skier when she skis down the track compare with the work done by gravity on the skier if she fell the same vertical height?

  A. Less work would be done on the skier when she skis down the track.

  B. More work would be done on the skier when she skis down the track.

  C. Equal amounts of work would be done.

  D. The answer depends on the angle of the track.

  Correct Answer: C

  The work done by gravity equals mgh, where m is the object's mass, g is the acceleration due to gravity, and h is the vertical distance. The work depends only on the vertical distance and is independent of the actual path taken. When the work done by a force is independent of the actual path taken, the force is said to be a conservative force.

• Question 332:

  Aski jump is an inclined track from which a ski jumper takes off through the air. After traveling down the track, the skier takes off from a ramp at the bottom of the track. The skier lands farther down on the slope.

  Figure 1 shows a ski jump, in which the ramp at the lower end of the track makes an angle of 30° to the horizontal. The track is inclined at an angle of to the horizontal and the slope is inclined at an angle of 45° to the horizontal. A ski jumper is stationary at the top of the track. Once the skier pushes off, she accelerates down the track, and then takes off from the ramp. The vertical height difference between the top of the track and its lowest point is 50 m, and the vertical height difference between the top of the ramp and its lowest point is 10 m.

  

  Figure 1

  The distance traveled by the skier between leaving the ski jump ramp and making contact with the slope is called the jump distance. In some cases, in order to increase the jump distance a skier will jump slightly upon leaving the ramp,

  thereby increasing the vertical velocity. Unless otherwise stated, assume that friction between the skis and the slope is negligible, and ignore the effects of air resistance.

  Another ski jumper sets off from a point farther down the jump track, and leaves the ramp at a speed of 16 m/s. If the time in flight is 4 s, what is the total horizontal distance traveled by the ski jumper after leaving the ramp?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: C

  In this question we are told that the ski jumper leaves the jump slope at a speed of 16 m/s, and that she remains in flight for a time of 4 seconds. Using this information, we need to find the horizontal distance traveled. Now in the horizontal direction, there are no forces acting on the ski jumper; so the horizontal distance traveled is equal to the horizontal speed times the total time in flight. We know the total time in flight, but don't have a value for the horizontal velocity. However,

  

  we do have the total velocity, and we know the angle at which she leaves the jump slope. So we can use the equation , where Vn is the horizontal component of velocity, Vt is the total velocity, and is the angle measured with respect to the horizontal. Substituting in known values, we get that the horizontal velocity Vn = 16 cos 30? which equals 16 , or 8 m/s. Using this we can calculate the horizontal distance traveled, and we get that the horizontal distance

  

  

  traveled equals meters, choice C.

• Question 333:

  Aski jump is an inclined track from which a ski jumper takes off through the air. After traveling down the track, the skier takes off from a ramp at the bottom of the track. The skier lands farther down on the slope.

  Figure 1 shows a ski jump, in which the ramp at the lower end of the track makes an angle of 30?to the horizontal. The track is inclined at an angle of to the horizontal and the slope is inclined at an angle of 45?to the horizontal. A ski jumper is stationary at the top of the track. Once the skier pushes off, she accelerates down the track, and then takes off from the ramp. The vertical height difference between the top of the track and its lowest point is 50 m, and the vertical height difference between the top of the ramp and its lowest point is 10 m.

  

  Figure 1

  The distance traveled by the skier between leaving the ski jump ramp and making contact with the slope is called the jump distance. In some cases, in order to increase the jump distance a skier will jump slightly upon leaving the ramp,

  thereby increasing the vertical velocity. Unless otherwise stated, assume that friction between the skis and the slope is negligible, and ignore the effects of air resistance.

  How would the speed of a skier leaving the jump ramp change if the vertical height of the jump ramp were increased from its original height of 10 meters?

  A. increase

  B. decrease

  C. remain the same

  D. The answer depends on the incline angle of the jump ramp.

  Correct Answer: B

  This question is testing your knowledge of the conservation of energy. When the skier is at the top of the track, she is not moving so all her energy is potential energy. At the top of the track she has potential energy. When she leaves the jump ramp, she is moving. So she has kinetic energy equal to 1/2 mv2. The difference in height between the top of the track and the point on the jump ramp where she jumps from is proportional to the amount of potential energy that gets converted to kinetic energy. Let h equal the height of the platform at the top of the track minus the height of the top of the jump ramp. The greater h is, the more potential energy gets converted to kinetic energy, and the greater the skier's speed when

  

  she jumps. Specifically, neglecting friction and air resistance, mgh = 1/2 mv2, and solving for v, we find that v = . In the question stem, we are told that the height of the ski jump ramp is increased; so h is decreased. Since v = , we see that a decrease in h corresponds to a decrease in v. Therefore, choice B is correct. You might have chosen answer choice A if you were careless and thought the track height increased.

• Question 334:

  Every atomic orbital contains plus and minus regions, defined by the value of the quantum mechanical function for electron density. When orbitals from different atoms overlap to form bonds, an equal number of new molecular orbitals results. These are of two types: or bonding orbitals, formed by overlap between orbital regions with the same sign, and antibonding * or * orbitals, formed by overlap between regions with opposite signs. Bonding orbitals have lower energy than their component atomic orbitals, and antibonding orbitals have higher energy. The electron pairs reside in the lower-energy bonding orbitals; the higher-energy, less stable orbitals remain empty when the molecule is in its ground state. A benzene ring has six unhybridized pz orbitals (one from each carbon atom), which together from six molecular orbitals, each one delocalized over the entire ring. Of the possible orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. The six electrons occupying the orbitals fill the three most stable molecular orbitals, leaving the other three empty. Molecular orbitals are filled from the lowest to the highest energy level. The number of bonds between atoms is determined by the number of filled bonding orbitals minus the number of filled antibonding orbitals; each antibonding orbital cancels out a filled bonding orbital. For a diatomic molecule, orbitals in the n = 2 energy level are filled as follows:

  

  (equal in energy), and * (equal in energy), *2 . (The designation of the three p orbitals as , , and are interchangeable.) Absorption of a photon can raise an electron to a higher-energy molecular orbital. The excited electron does not immediately change its spin, which is opposite to that of the electron with which it was previously paired. This singlet state is relatively unstable: the molecule may interact with another molecule, or fluoresce and return to its ground state. Alternatively, there may be a change in spin direction somewhere in the system; the molecule then enters the so-called triplet state, which generally has lower energy. The molecule now cannot return quickly to its ground state, since the excited electron no longer has a partner of opposite spin with which to pair. It also cannot return to the singlet state, because the singlet has greater energy. Consequently, the triplet state, which has two unpaired electrons in separate orbitals, is long-lived by atomic standards, with a lifetime that may be ten seconds or more. During this period, the molecule is highly reactive.

  The quantum number that distinguishes the px orbital from the py orbital is called the:

  A. azimuthal quantum number.

  B. magnetic quantum number.

  C. principal quantum number.

  D. spin quantum number.

  Correct Answer: B

  This is straightforward question relying on your knowledge of quantum numbers. The first quantum number, n, is called the principal quantum number and determines which principal energy level the electron is in, n = 1, n = 2 etc. This does not help specify between the px and py orbital, thus it is not the answer we are looking for. The second quantum number is the azimuthal number designated by l. This determines the subshell s, p, d or f. The azimuthal quantum number can also be referred to as the angular momentum quantum number. Choice A is the azimuthal quantum number, and it does not help us distinguish the px orbital from the py orbital, so we can rule choice A out. The third quantum number, the magnetic quantum number specifies the particular orbitals within a subshell and is given by ml. Each of these orbitals can hold two electrons. There's only one orbital in an s subshell, in a p subshell there are three, in a d subshell there are five, and in an f subshell there are seven. The three p orbitals are known as px, py, and pz. The magnetic quantum number allows you to differentiate between the px and the py orbital, so choice B is the correct answer. The fourth quantum number, known as ms, tells us whether the electron has a plus or minus spin. Each orbital when filled contains two electrons of opposite spins. Thus it is choice B, the magnetic quantum number, ml, that distinguishes the x, y, and z orbitals of the p subshell.

• Question 335:

  Every atomic orbital contains plus and minus regions, defined by the value of the quantum mechanical function for electron density. When orbitals from different atoms overlap to form bonds, an equal number of new molecular orbitals results. These are of two types: or bonding orbitals, formed by overlap between orbital regions with the same sign, and antibonding * or * orbitals, formed by overlap between regions with opposite signs. Bonding orbitals have lower energy than their component atomic orbitals, and antibonding orbitals have higher energy. The electron pairs reside in the lower-energy bonding orbitals; the higher-energy, less stable orbitals remain empty when the molecule is in its ground state. A benzene ring has six unhybridized pz orbitals (one from each carbon atom), which together from six molecular orbitals, each one delocalized over the entire ring. Of the possible orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. The six electrons occupying the orbitals fill the three most stable molecular orbitals, leaving the other three empty. Molecular orbitals are filled from the lowest to the highest energy level. The number of bonds between atoms is determined by the number of filled bonding orbitals minus the number of filled antibonding orbitals; each antibonding orbital cancels out a filled bonding orbital. For a diatomic molecule, orbitals in the n = 2 energy level are filled as follows:

  

  (equal in energy), and * (equal in energy), *2 . (The designation of the three p orbitals as , , and are interchangeable.) Absorption of a photon can raise an electron to a higher-energy molecular orbital. The excited electron does not immediately change its spin, which is opposite to that of the electron with which it was previously paired. This singlet state is relatively unstable: the molecule may interact with another molecule, or fluoresce and return to its ground state. Alternatively, there may be a change in spin direction somewhere in the system; the molecule then enters the so-called triplet state, which generally has lower energy. The molecule now cannot return quickly to its ground state, since the excited electron no longer has a partner of opposite spin with which to pair. It also cannot return to the singlet state, because the singlet has greater energy. Consequently, the triplet state, which has two unpaired electrons in separate orbitals, is long-lived by atomic standards, with a lifetime that may be ten seconds or more. During this period, the molecule is highly reactive.

  Molecular orbitals in hydrocarbons are formed between the 1s atomic orbital of hydrogen and the sp, sp2, or sp3 hybrid atomic orbitals of carbon. Which choice correctly lists the energy level of the C-H bonds, from lowest to highest?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: D

  To answer this question, you will have to remember the types of hybrid atomic orbitals formed by these simple organic molecules. In CH4, methane, the single 2s orbital and the three 2p orbitals hybridize to form an sp3 hybrid orbital. In C2H2, the 2s orbital hybridizes with only two of the p orbitals to form an sp2 hybrid. The third p orbital remains separate and forms the second carbon-carbon bond. In C6H6, benzene, the six carbons also form sp2 hybrid orbitals and the remaining p orbitals form the pi electron cloud above and below the plane of the ring. In C2H2, acetylene, only one p orbital hybridizes with the s orbital, and the two remaining p orbitals form the second and third carbon-carbon bonds. The C-H bonds of each of these molecules are formed by the hybrid sp, sp2 or sp3 orbitals. Since the s subshell is lower energy than the p subshell, the greater the s character of an orbital, the lower its energy will be. Thus, the energy level transition from lowest to highest will go from sp to sp2 or sp3, choice D.

• Question 336:

  Every atomic orbital contains plus and minus regions, defined by the value of the quantum mechanical function for electron density. When orbitals from different atoms overlap to form bonds, an equal number of new molecular orbitals results. These are of two types: or bonding orbitals, formed by overlap between orbital regions with the same sign, and antibonding * or * orbitals, formed by overlap between regions with opposite signs. Bonding orbitals have lower energy than their component atomic orbitals, and antibonding orbitals have higher energy. The electron pairs reside in the lower-energy bonding orbitals; the higher-energy, less stable orbitals remain empty when the molecule is in its ground state. A benzene ring has six unhybridized pz orbitals (one from each carbon atom), which together from six molecular orbitals, each one delocalized over the entire ring. Of the possible orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. The six electrons occupying the orbitals fill the three most stable molecular orbitals, leaving the other three empty. Molecular orbitals are filled from the lowest to the highest energy level. The number of bonds between atoms is determined by the number of filled bonding orbitals minus the number of filled antibonding orbitals; each antibonding orbital cancels out a filled bonding orbital. For a diatomic molecule, orbitals in the n = 2 energy level are filled as follows:

  

  (equal in energy), and * (equal in energy), *2 . (The designation of the three p orbitals as , , and are interchangeable.) Absorption of a photon can raise an electron to a higher-energy molecular orbital. The excited electron does not immediately change its spin, which is opposite to that of the electron with which it was previously paired. This singlet state is relatively unstable: the molecule may interact with another molecule, or fluoresce and return to its ground state. Alternatively, there may be a change in spin direction somewhere in the system; the molecule then enters the so-called triplet state, which generally has lower energy. The molecule now cannot return quickly to its ground state, since the excited electron no longer has a partner of opposite spin with which to pair. It also cannot return to the singlet state, because the singlet has greater energy. Consequently, the triplet state, which has two unpaired electrons in separate orbitals, is long-lived by atomic standards, with a lifetime that may be ten seconds or more. During this period, the molecule is highly reactive.

  Which of the following figures describes the shape of *2pz molecular orbital?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: A

  The molecular orbital you have been asked to choose is an antibonding sigma orbital. Examining the question, the star above the sigma sign indicates that the orbital is antibonding. You should know that sigma orbitals are formed in a straight line; choice D is a bonding sigma orbital and choice A, the correct choice, is an antibonding sigma orbital. In pi orbitals, the lobes of the p orbitals are perpendicular to the line connecting the two atoms. When a pi orbital is bonding, the lobes above and below the plane of the molecule connect to form a shape such as that shown in choice B. When a pi orbital is antibonding, the perpendicular p lobes cancel each other out where they overlap. This produces an electron cloud that looks as if the p orbitals were repelling each other, as in choice C.

• Question 337:

  Every atomic orbital contains plus and minus regions, defined by the value of the quantum mechanical function for electron density. When orbitals from different atoms overlap to form bonds, an equal number of new molecular orbitals results. These are of two types: or bonding orbitals, formed by overlap between orbital regions with the same sign, and antibonding * or * orbitals, formed by overlap between regions with opposite signs. Bonding orbitals have lower energy than their component atomic orbitals, and antibonding orbitals have higher energy. The electron pairs reside in the lower-energy bonding orbitals; the higher-energy, less stable orbitals remain empty when the molecule is in its ground state. A benzene ring has six unhybridized pz orbitals (one from each carbon atom), which together from six molecular orbitals, each one delocalized over the entire ring. Of the possible orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. The six electrons occupying the orbitals fill the three most stable molecular orbitals, leaving the other three empty. Molecular orbitals are filled from the lowest to the highest energy level. The number of bonds between atoms is determined by the number of filled bonding orbitals minus the number of filled antibonding orbitals; each antibonding orbital cancels out a filled bonding orbital. For a diatomic molecule, orbitals in the n = 2 energy level are filled as follows:

  

  (equal in energy), and * (equal in energy), *2 . (The designation of the three p orbitals as , , and are interchangeable.) Absorption of a photon can raise an electron to a higher-energy molecular orbital. The excited electron does not immediately change its spin, which is opposite to that of the electron with which it was previously paired. This singlet state is relatively unstable: the molecule may interact with another molecule, or fluoresce and return to its ground state. Alternatively, there may be a change in spin direction somewhere in the system; the molecule then enters the so-called triplet state, which generally has lower energy. The molecule now cannot return quickly to its ground state, since the excited electron no longer has a partner of opposite spin with which to pair. It also cannot return to the singlet state, because the singlet has greater energy. Consequently, the triplet state, which has two unpaired electrons in separate orbitals, is long-lived by atomic standards, with a lifetime that may be ten seconds or more. During this period, the molecule is highly reactive.

  Given the order in which orbitals are filled, which molecule is a triplet in its ground state?

  

  A. Option A

  B. Option B

  C. Option C

  D. Option D

  Correct Answer: B

  The answer to this question is found in the passage: You are given the order of orbital filling in paragraph three and are told in the last paragraph what a triplet state is. Remember that when there are orbitals of equal energy, each one will be half-filled before any of the orbitals is completely filled, and all the half-filled orbitals will have electrons with the same spin. Looking at the answer choices for the question, you can see that they are all diatomic; thus, there will be two electrons in a hydrogen molecule, fourteen in nitrogen, sixteen in oxygen and eighteen in fluorine. The passage does not describe how to fill the n = 1 shell, but from knowing that the n = 2 shell has the sigma 2s bonding orbitals and one sigma 2s antibonding orbital, there will be sigma bonding and antibonding orbitals in the n = 1 shell, and these will also hold four electrons. Therefore, molecular hydrogen will fill half the n = 1 shell with the total of two electrons that it has and there will be zero electrons in its second shell. Working in a similar way you will have ten electrons in the second shell for molecular nitrogen, twelve for oxygen, and fourteen for fluorine. When you fill in the molecular orbitals, you will find that nitrogen just fills the pi 2x and 2y bonding orbitals. Since there are no unpaired electrons, molecular nitrogen can't be a triplet. Molecular oxygen has two extra electrons, which go into the pi 2x and 2y antibonding orbitals. In other words, it has unpaired electrons with the same spin. If you’re not sure, check the final choice: In fluorine, these pi 2x and 2y antibonding orbitals are filled with the two extra electrons, so fluorine is not a triplet. Thus, it turns out that the oxygen molecule is a triplet in its ground state, so choice B is the correct answer.

• Question 338:

  Every atomic orbital contains plus and minus regions, defined by the value of the quantum mechanical function for electron density. When orbitals from different atoms overlap to form bonds, an equal number of new molecular orbitals results. These are of two types: or bonding orbitals, formed by overlap between orbital regions with the same sign, and antibonding * or * orbitals, formed by overlap between regions with opposite signs. Bonding orbitals have lower energy than their component atomic orbitals, and antibonding orbitals have higher energy. The electron pairs reside in the lower-energy bonding orbitals; the higher-energy, less stable orbitals remain empty when the molecule is in its ground state. A benzene ring has six unhybridized pz orbitals (one from each carbon atom), which together from six molecular orbitals, each one delocalized over the entire ring. Of the possible orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. The six electrons occupying the orbitals fill the three most stable molecular orbitals, leaving the other three empty. Molecular orbitals are filled from the lowest to the highest energy level. The number of bonds between atoms is determined by the number of filled bonding orbitals minus the number of filled antibonding orbitals; each antibonding orbital cancels out a filled bonding orbital. For a diatomic molecule, orbitals in the n = 2 energy level are filled as follows:

  

  (equal in energy), and * (equal in energy), *2 . (The designation of the three p orbitals as , , and are interchangeable.) Absorption of a photon can raise an electron to a higher-energy molecular orbital. The excited electron does not immediately change its spin, which is opposite to that of the electron with which it was previously paired. This singlet state is relatively unstable: the molecule may interact with another molecule, or fluoresce and return to its ground state. Alternatively, there may be a change in spin direction somewhere in the system; the molecule then enters the so-called triplet state, which generally has lower energy. The molecule now cannot return quickly to its ground state, since the excited electron no longer has a partner of opposite spin with which to pair. It also cannot return to the singlet state, because the singlet has greater energy. Consequently, the triplet state, which has two unpaired electrons in separate orbitals, is long-lived by atomic standards, with a lifetime that may be ten seconds or more. During this period, the molecule is highly reactive.

  Among conjugated polyenes (molecules with alternating carbon-carbon double and single bonds) why are those that are longer able to absorb longer wavelengths of light?

  A. Larger molecular orbitals have a lower ground state.

  B. A longer wavelength is better able to interact with a longer molecular orbital.

  C. The larger number of molecular orbitals allows for smaller energy transitions.

  D. Larger molecular orbitals can absorb more energy.

  Correct Answer: C

  The key to this question is found in the discussion in Chapter 1 of your Physical Sciences Review Notes where you are told that a photon of light can be absorbed only if its energy level is equal to the change in energy between two orbitals in the atom or molecule. Longer wavelengths of light have a lower frequency and thus lower energy level, so you can eliminate choice D immediately. The wavelength of light does not have to fit the length of the molecule, so choice B is wrong. This leaves you with choices A and C. To decide between these choices, think about what determines the energy of a quantum of light absorbed by an atom or molecule. The energy of the photon must be equal to the difference in energy between the ground state and the excited state. What is important is not the absolute energy level of the ground state, but the difference in energy level between the lower and higher orbital. Longer conjugated polyenes have a greater number of p electrons forming pi orbitals, and therefore a greater number of possible molecular orbitals. This produces smaller energy transitions, allowing for absorption of photons at a lower energy and longer wavelength. Thus, choice C is correct.

• Question 339:

  Every atomic orbital contains plus and minus regions, defined by the value of the quantum mechanical function for electron density. When orbitals from different atoms overlap to form bonds, an equal number of new molecular orbitals results. These are of two types: bonding orbitals, formed by overlap between orbital regions with the same sign, and antibonding * or * orbitals, formed by overlap between regions with opposite signs. Bonding orbitals have lower energy than their

  component atomic orbitals

  ,

  or

  and antibonding orbitals have higher energy. The electron pairs reside in the lower-energy bonding orbitals; the higher-energy, less stable orbitals remain empty when the molecule is in its ground state. A benzene ring has six unhybridized pz (one from each carbon atom), which together from six molecular orbitals, each one delocalized over the entire ring. Of the possible orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. The six electrons occupying the orbitals fill the three most stable molecular orbitals, leaving the other three empty. Molecular orbitals are filled from the lowest to the highest energy level. The number of bonds between atoms is determined by the number of filled bonding orbitals minus the number of filled antibonding orbitals; each antibonding orbital

  

  cancels out a filled bonding orbital. For a diatomic molecule, orbitals in the n = 2 energy level are filled as follows: , , 2 , and (equal in energy), and * (equal in energy), *2 . (The designation of

  

  the three p orbitals as , , and are interchangeable.) Absorption of a photon can raise an electron to a higher-energy molecular orbital. The excited electron does not immediately change its spin, which is opposite to that of the electron with which it was previously paired. This singlet state is relatively unstable: the molecule may interact with another molecule, or fluoresce and return to its ground state. Alternatively, there may be a change in spin direction somewhere in the system; the molecule then enters the so-called triplet state, which generally has lower energy. The molecule now cannot return quickly to its ground state, since the excited electron no longer has a partner of opposite spin with which to pair. It also cannot return to the singlet state, because the singlet has greater energy. Consequently, the triplet state, which has two unpaired electrons in separate orbitals, is long-lived by atomic standards, with a lifetime that may be ten seconds or more. During this period, the molecule is highly reactive.

  Which of the following four depictions of molecular orbitals represents the highest energy state for a 6- carbon polyene molecule? (The signs given are the signs for the mathematical functions defining the p orbitals on one side of the molecule.)

  A. – – – – – –

  B. + + + – – –

  C. + + – – + +

  D. + – + – + –

  Correct Answer: D

  Explanation: To answer this question, you need to understand what it is that causes a molecular orbital to have high energy. The first paragraph tells us that when orbitals from different atoms with the same sign overlap to form bonds, they are called bonding orbitals. Also, we are told that bonding orbitals have lower energy than their component atomic orbitals. In the same way, we can say that when orbitals from different atoms with opposite signs overlap, they form antibonding orbitals. Antibonding orbitals are higher in energy than the original atomic orbitals. The second paragraph tells us that of the possible pi orbital structures for benzene, the one with the lowest energy has the plus region of all six p orbital functions on one side of the ring. From this we can conclude that another situation for the lowest energy would be for the negative region of all six p orbital functions on the other side of the ring. In choice A, all the atomic orbitals have their negative sides facing the same direction, and this corresponds to the lowest energy molecular orbital--so we can rule out choice A, because this gives the lowest energy state. Because you are told that the lowest pi energy orbitals are the ones with the plus region of all six p orbital functions on one side of the ring, you should be able to deduce that the energy level of a molecular orbital is determined not by whether the function signs are positive or negative, but by whether adjacent atomic orbitals are of the same or opposite sign. Examining choice B, there is bonding from carbons one through three and four to six, but carbons three and four are antibonding. In choice C, carbons one to two, three to four and five to six are bonding but two to three and four to five are antibonding. Choice D is entirely antibonding, since there are no adjacent orbital functions of the same sign. Therefore, the molecular orbital portrayed in choice D has the highest energy level.

• Question 340:

  When light in the ultraviolet region of the spectrum is shone on a type of material known as a phosphor, it fluoresces and emits light in the visible region of the spectrum. Lamps that utilize this property, known as fluorescent lamps, are very efficient light sources. The arrangement of a typical fluorescent lamp is shown below. The lamp is a glass tube whose inside walls are covered with a phosphor. The tube has an appreciable length-to-diameter ratio so as to reduce the power losses at each end, and it is filled with argon gas mixed with mercury vapor. Inside each end of the tube are tungsten electrodes covered with an emission material.

  Electrons are liberated at the cathode and accelerated by an applied electric field. These free electrons encounter the gas mixture, ionizing some mercury atoms and exciting others. Since it requires more energy to ionize the atoms than to excite the electrons, more excitation than ionization occurs. When the excited electrons revert to their ground state, they radiate ultraviolet photons with a wavelength of 253.7 nm. These photons impinge on the phosphor coating of the tube and excite electrons in the phosphor to higher energy states. The excited electrons in the phosphor return to their ground state in two or more steps, producing radiation in the visible region of the spectrum. Not every fluorescent lamp emits the same color of radiation; the color is dependent on the relative percentages of different heavy metal compounds in the phosphor.

  The fluorescent lamp shown operates at 100 volts and draws 400 milliamps of current during normal operation. Of the total power that the lamp consumes, only 25% is converted to light, while the remaining 75% is dissipated as heat. This energy keeps the lamp at its optimum working temperature of 40°C. In the lamp shown, the phosphor coating is calcium metasilicate, which emits orange to yellow light.

  

  The lamp also emits a small proportion of ultraviolet light in addition to the light emitted in the visible spectrum. This ultraviolet light is incident on a metal that has a work function, which is the minimum energy necessary to free an electron, of

  2.00 eV. What will be the kinetic energy of an electron that is ejected from the metal if the frequency of the incident light is 1.2?015 Hz? (Note: h = 4.14?0-15 eV穝.)?

  A. 9.936 eV

  B. 6.948 eV

  C. 4.968 eV

  D. 2.968 eV

  Correct Answer: D

  This question tests your understanding of the photoelectric effect when light of a sufficiently high frequency is incident on a metal. The minimum frequency of light that can cause a metal to eject electrons is called the threshold frequency and can be determined from the work function of the metal to eject electrons is called the threshold frequency and can be determined from the work function of the metal. Therefore, an electron in the metal must receive at least 2.00 electron-volts of energy in order to be ejected. Any surplus energy will be converted to the kinetic energy of the electrons. The energy of the incident light is equal to Planck's constant, h, times its frequency. Here, the energy equals 4.14×10-15×1.2×1015, which is about 4.8 electron-volts. Incorrectly stopping at this point gives choice C, 4.968 electron-volts. However, this is incorrect: we still need to subtract the work function from the total energy of incident light because this is the energy the electron must use just to escape the metal. It won't contribute to the electron's kinetic energy. So the kinetic energy of the ejected electron is equal to the energy of the incident light minus the work function of the metal, or 4.8– 2 = 2.8 electron-volts. The closest answer is choice D, 2.968 electron-volts, choice D. Be careful! Wrong answer choices on the MCAT are often the results of incomplete solutions.