Question 1

In the double-slit experiment with monochromatic light, what does the observed pattern on the screen primarily demonstrate about the nature of light?

Accepted Answer

Light exhibits both wave and particle properties, as the interference pattern is built up by individual photon detections.

Question 2

According to the Heisenberg uncertainty principle, which of the following statements is correct?

Accepted Answer

The product of the uncertainties in position and momentum must be greater than or equal to $$\frac{\hbar}{2}$$: $$\Delta x \Delta p_x \geq \frac{\hbar}{2}.$$

Question 3

In a single-slit diffraction experiment, if the slit width $$a is $$decreased, what happens to the uncertainty in the photon's momentum component $$p_y$$ perpendicular to the slit?

Accepted Answer

The uncertainty in $$p_y$$ increases.

Question 4

Which equation correctly relates the wavelength $$\lambda of a $$photon to its momentum $$p$$?

Accepted Answer

$$\lambda = \frac{h}{p}$$

Question 5

A photon passes through a slit of width $$a. $$What is the minimum uncertainty in its momentum component perpendicular to the slit ($$\Delta p_y$$)?

Accepted Answer

$$\Delta p_y \geq \frac{h}{a}$$

Question 6

If a photon's wave function is a perfect sine wave extending infinitely in space, what can be said about the uncertainty in its position ($$\Delta x) $$and momentum ($$\Delta p_x$$)?

Accepted Answer

$$\Delta x is $$infinite and $$\Delta p_x = 0$$

Question 7

Which of the following best describes the effect of superimposing two sinusoidal waves of slightly different frequencies?

Accepted Answer

The resulting wave is more localized in time, but has two possible energy values.

Question 8

In the context of the Heisenberg uncertainty principle, what does the shaded region in the $$\Delta x vs$$. $$\Delta p_x$$ plot represent?

Accepted Answer

The region where $$\Delta x \Delta p_x \geq \frac{\hbar}{2}$$, which is physically allowed.

Question 9

Which of the following is a correct statement about the probability distribution observed in a single-photon double-slit experiment?

Accepted Answer

The pattern emerges statistically as many photons are detected, reflecting the probability distribution predicted by wave theory.

Question 10

Which equation expresses the Heisenberg uncertainty principle for energy and time?

Accepted Answer

$$\Delta E \Delta t \geq \frac{\hbar}{2}$$

Question 11

A photomultiplier detector is used to measure the arrival of photons in a double-slit experiment. What does the detection event represent in quantum theory?

Accepted Answer

The collapse of the photon's wave function at a specific location.

Question 12

If the wavelength $$\lambda of $$light used in a single-slit experiment is much smaller than the slit width $$a$$, what can be said about the angular position $$\$$theta_1$$ of the first minimum?

Accepted Answer

$$\sin \$$theta_1$$ \approx \frac{\lambda}{a}$$, so $$\$$theta_1$$ is small.

Question 13

Which of the following best explains why narrowing the slit in a single-slit diffraction experiment increases the spread of the diffraction pattern?

Accepted Answer

Narrowing the slit decreases the uncertainty in the photon's position, which increases the uncertainty in its momentum.

Question 14

A photon is described by a wave packet formed by superimposing many sinusoidal waves with different wavelengths. What does this imply about the uncertainties in its position and momentum?

Accepted Answer

The photon has a more localized position but a greater uncertainty in momentum.

Question 15

In the context of quantum mechanics, what does the probability distribution of photon detections on a screen represent?

Accepted Answer

The likelihood of finding a photon at a particular location, as determined by the square of the wave function's amplitude.

Question 16

Which of the following is a direct consequence of the Heisenberg uncertainty principle for energy and time?

Accepted Answer

The more precisely the energy of a system is known, the less precisely the time interval during which it has that energy can be known.

Wave-Particle Duality, Probability, and the Heisenberg Uncertainty Principle

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