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GRE Subject Test: Physics : Quantum Mechanics and Atomic Physics

Study concepts, example questions & explanations for GRE Subject Test: Physics

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All GRE Subject Test: Physics Resources

33 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Quantum Mechanics And Atomic Physics

Which of the following wavelengths could be used to measure the position of an electron with the greatest accuracy?

Possible Answers:

Gamma-rays

X-ray

Red light

Infared

Radio

Correct answer:

Gamma-rays

Explanation:

The Heisenberg Uncertainty principle states that

$\Delta x \Delta p \ge \frac{\hbar}{2}.$

Therefore, the smallest wavelength will have the lowest uncertainty in the position. Thus, we must pick the regime of options given which has the lowest wavelength. That is gamma-ray.

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Example Question #1 : Quantum Mechanics And Atomic Physics

What wavelength will result in the most accurate measurement of the momentum of an electron?

Possible Answers:

Red light

Infrared

X-ray

Gamma-ray

Radio

Correct answer:

Radio

Explanation:

The Heisenberg Uncertainty Principle states that:

$\Delta x \Delta p \ge \frac{\hbar}{2}.$ Since the uncertainty in the position is inversely proportional to the uncertainty in the momentum, we need to pick the longest wavelength. Of the options listed, radio has the longest wavelength.

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Example Question #1 : Square Wells/Particle In A Box

If a ground state particle is in a one-dimension square well, where is the probability of finding the particle equal to zero?

Possible Answers:

$\frac{1}{3}$ the way in the box.

None of these

At the boundary.

$\frac{1}{4}$ the way in the box.

In the middle.

Correct answer:

At the boundary.

Explanation:

This is a fundamental concept question. For a ground state particle, the only place where the probability is equal to zero is at the boundary because the particle cannot be found there. He has to be in the box (not unlike a cat).

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Example Question #1 : Quantum Mechanics And Atomic Physics

What is the energy of the photon emitted when a Hydrogen atom makes a transition from the n=4 to the n=2 atomic energy level?

Possible Answers:

3.4 eV

5.95eV

6.8eV

2.55 eV

13.6eV

Correct answer:

2.55 eV

Explanation:

$E=-13.6eV(\frac{1}{n_f^2}-\frac{1}{n_i^2})$ , where refers to the final and initial energy levels, respectively.

$E=-13.6eV(\frac{1}{2^2}-\frac{1}{4^2})=-13.6eV\frac{3}{16}=-2.55eV.$

However, since the question asked what is the energy of the photon, it is the absolute value of the energy calculated above because of conservation of energy. The photon carries away the energy lost by the atom.

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Example Question #4 : Quantum Mechanics And Atomic Physics

What color will be emitted in the n=5 to n=2 transition in the Hydrogen Balmer series?

Possible Answers:

Red

Blue

Violet

Yellow

Green

Correct answer:

Violet

Explanation:

$\frac{1}{\lambda}=R(\frac{1}{m^2}-\frac{1}{n^2})$ .

Here, $\lambda$ is the wavelength, $R (1.097 *10^7 m^{-1})$ is the Rydberg constant, m=2 for the Balmer series, and refers to the upper atomic level (this is in this case). Now, we just need to plug everything in, and solve for wavelength.

$\frac{1}{\lambda}=(1.097\;x\;10^7)(\frac{1}{2^2}-\frac{1}{5^2}).$

$\frac{1}{\lambda}=(1.097\;x\;10^7)(\frac{21}{100})=2303700m^{-1}.$

By inverting, $\lambda=4.34\;x\;10^{-7}m=434nm.$ This is in the violet regime of the visible spectrum.

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All GRE Subject Test: Physics Resources

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GRE Subject Test: Physics : Quantum Mechanics and Atomic Physics

Study concepts, example questions & explanations for GRE Subject Test: Physics

All GRE Subject Test: Physics Resources

Example Questions

Example Question #1 : Quantum Mechanics And Atomic Physics

Example Question #1 : Quantum Mechanics And Atomic Physics

Example Question #1 : Square Wells/Particle In A Box

Example Question #1 : Quantum Mechanics And Atomic Physics

Example Question #4 : Quantum Mechanics And Atomic Physics

All GRE Subject Test: Physics Resources

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