Question

I.(20p) Fill the following spaces with or circle the appropriate answers (can be more than one!).

I.1. In Tom's frame of reference, two events A and B take place at different locations along the x axis but are observed by Tom to be simultaneous. Which of the following statements is true?
(1) No observers moving relative to Tom will find A and B to be simultaneous, but some may see A before B and others B before A.

(2) No observers moving relative to Tom will find A and B to be simultaneous, but they all will observe events A and B in the same order.
(3) All observers moving relative to Tom will also perceive A and B to be simultaneous.
(4) Some observers moving relative to Tom will find A and B to be simultaneous, while others will not.

I.2. The Pauli principle states that
(1) Atoms emit photons when electrons change from one quantum state to another. (2) No two electrons in an atom can have the same set of quantum numbers.
(3) Electrons in an atom are forbidden from occupying certain orbits.
(4) An atom with Z positive charges in its nucleus cannot hold more than Z electrons.

I.3. The photoelectric effect:
(1) verifies that electrons behave like waves. (2) involves the interference of light waves that reflect from the surface of a metal. (3) is consistent only with the wave theory of light.
(4) verifies that light behaves as if it is composed of particles.

I.4. Which is the correct procedure for combining the wave functions of the two electrons in the H2 molecule to get the total electron probability density?
(1) First add (or subtract) the two individual wave functions, then square the result; that is, | ψ1 ± ψ2|2. (2) First square the two wave functions, then add or subtract the results; that is,|ψ1|2 ± | ψ2|2.

I.5. In the ground state of a sodium atom, which has 11 electrons, the valence electron goes into the 3s state rather than the 3p state because:
(a) the 3s state is lower in energy than the 3p state. (b) the 3p state is already filled with electrons. (c) the 3s orbit occupies less space than the 3p orbit.

(d) the 3s orbit is always closer to the nucleus than the 3p orbit.

I.6. The sodium atom (Z = 11) has a single valence electron in the 3s subshell. The properties of the electron can be analyzed as if the electric force acting on that electron were due to an effective charge of about (a) +e (b) –e (c) +5e (d) +10e

1.7. X-rays can be produced by ____________.
a. hydrogen atoms; b. silver atoms; c. platinum atoms; d. all atoms.

I.8. In which states of hydrogen is the probability to locate the electron independent of the direction in space?
(1) None (2) Only the n = 1 state (3) Only ml states (4) All l = 0 states

I.9. Molecules have three different types of excited states: electronic, vibrational, rotational. Put these in decreasing order according to the amount of energy generally required for each type of excitation.
(1) Vibrational, electronic, rotational (2) Vibrational, rotational, electronic
(3) Electronic, vibrational, rotational (4) Electronic, rotational, vibrational

(5) Rotational, electronic, vibrational (6) Rotational, vibrational, electronic

1

2 I.10. A beam of particles is incident from the negative x direction on a potential energy step at x = 0.

When x < 0, the potential energy of the particles is zero, and for x > 0 the potential energy has the constant positive value U0. In the region x < 0, the particles have a kinetic energy K that is smaller than U0. What is the form of the wave function in the region x > 0?
(a)Aekx + Be−kx (b) Aeikx + Be−ikx (c) Aekx (d) Ae−kx (e) Acos kx + Bsin kx

I.11. Einstein’s “Classic” tests proposed in1915 for general relativity are:
1) Precession of perihelion of Mercury. 2) Light is bent in a gravitational field. 3) Clocks run slow in gravitational field (“gravitational time dilation” or “gravitational redshift”). 4) All the above.

Answer 1

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