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MCAT Sample Questions : Physical Sciences

Passage III

When X-rays are produced in an X-ray tube, two types of X-ray spectra are observed: continuous spectra and line spectra.

A continuous spectrum is produced by bremsstrahlung, the electromagnetic radiation produced when free electrons are accelerated during collisions with ions.

A line spectrum results when an electron having sufficient energy collides with a heavy atom, and an electron in an inner energy level is ejected from the atom.An electron from an outer energy level then fills the vacant inner energy level, resulting in emission of an X-ray photon.For example, if an electron in the n = 1 energy level is ejected from an atom, an electron in the n = 2 level of the atom can fill the vacancy created in the n = 1 level, and a photon with an energy equal to the energy difference between the two levels will be emitted.

A scientist produced both types of spectra using the X-ray tube shown in Figure 1 below.

Figure 1 Heated cathode X-ray tube

The tube contains a heated filament cathode (C), which emits electrons.A power supply (LV) regulates the filament temperature, the electrical current in the tube, and the number of X-rays produced at the anode (A).Another power supply (HV) regulates electron acceleration.

The scientist used an X-ray tube to determine the relationship between X-ray wavelength, ?, and X-ray intensity, I, which is proportional to the number of X-ray photons emitted at ?.The scientist then graphed the results of the experiment, as shown in Figure 2.

Figure 2 X-ray intensity versus wavelength

Some sample questions on this passage are as follows:

  1. In Figure 2, which of the following represents the source of emission peaks P1 and P2?

    1. Bremsstrahlung
    2. Absorption of X-ray photons resulting in electronic excitations in atoms
    3. Emission of X-ray photons as a result of electronic transitions in atoms
    4. Acceleration of electrons in a magnetic field

    Answer: C

    Explanation: The emission peaks P1 and P2 are described in the passage as due to an electron from an outer energy level filling a vacant inner energy level, resulting in emission of an X-ray photon. These photons have discrete energies, and therefore discrete wavelengths, so they appear in the spectrum as peaks. Thus, answer choice C is the best answer.

  2. Based on the tube in Figure 1, to maintain an electron current of 0.005 A and a potential drop of 105 V between the anode and the cathode, approximately how much power must the tube consume?

    1. 5 x 102 W
    2. 1 x 103 W
    3. 2 x 105 W
    4. 2 x 107 W

    Answer: A

    Explanation: The power P, supplied by the battery to accelerate the electron beam is given by the formula P = IV, where I is the beam current and V is the potential difference between the cathode and anode. Therefore P = (5 x 10-3 A) x (105 V) = 5 x 102 W. Therefore, answer choice A is the best answer.

  3. The ionization potentials for electrons in the n = 1, 2, and 3 energy levels of Pb are 1,400 x 10-17 J, 240 x 10-17 J, and 48 x 10-17 J, respectively.When an electron in the n = 2 level fills a vacancy in the n = 1 level, what is the energy of the X ray that is emitted?

    1. 1.92 x 10-15 J
    2. 2.40 x 10-15 J
    3. 1.16 x 10-14 J
    4. 1.40 x 10-14 J

    Answer: C

    Explanation: The emitted X-ray has the positive energy difference between the atomic energy levels as measured by their ionization potentials. For Pb n = 2 to 1, that is (1,400 x 10-17 J) - (240 x 10-17 J) = 1160 x 10-17 J = 1.16 x 10-14 J. Thus, answer choice C is the best answer.

  4. According to the passage, bremsstrahlung will NOT be produced by collisions between electrons and:

    1. He
    2. He2+
    3. Li1+
    4. protons

    Answer: A

    Explanation: According to the passage, bremsstrahlung is produced when electrons are accelerated during collisions with ions. All the choices of answers are ions except He, a neutral atom. Therefore, answer choice A is the correct answer.

  5. n order to increase the maximum kinetic energy of electrons colliding with the anode, the scientist made which of the following changes?

    1. The voltage of HV was increased.
    2. The voltage of HV was decreased.
    3. The voltage of LV was increased.
    4. The voltage of LV was decreased.

    Answer: A

    Explanation: To increase the kinetic energy of the electrons, they must be accelerated by a higher voltage between the cathode and anode, thus the voltage of HV was increased. Thus, answer choice A is the best answer.

  6. n Figure 2, peaks P1 and P2were produced by events that occurred with unequal probabilities.Which peak was produced by the more probable event?

    1. P1, because the peak has the longer wavelength
    2. P1, because the peak has the lower intensity
    3. P2, because the peak has the longer wavelength
    4. P2, because the peak has the higher intensity

    Answer: D

    Explanation: The probability of an X-ray emission event at a given wavelength is measured by its intensity in the spectrum. In Figure 2, P2 has a higher intensity than does P1. Thus, answer choice D is the best answer

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