Q: A photon has a wavelength of $$500\ \text{nm}. $$What is its energy?

$$E = \frac{hc}{\lambda} = \frac{(6.626 \times 10$$^{-34}$$\ \text{J}\cdot\text{s})(3.00 \times 10^8$\ \text{m/s})}{500 \times 10$$^{-9}$$\ \text{m}} \approx 3.98 \times 10$$^{-19}$$\ \text{J}$$

Question 1

Which of the following best describes Planck's hypothesis regarding black body radiation?

Accepted Answer

Energy is emitted in discrete packets called quanta, with energy $$E = h 
u.$$

Question 2

A photon has a wavelength of $$500\ 	ext{nm}. $$What is its energy?

Accepted Answer

$$E = \frac{hc}{\lambda} = \frac{(6.626 	imes 10$$^{-34}$$\ 	ext{J}\cdot	ext{s})(3.00 	imes 10^8$\ 	ext{m/s})}{500 	imes 10$$^{-9}$$\ 	ext{m}} \approx 3.98 	imes 10$$^{-19}$$\ 	ext{J}$$

Question 3

Which experiment provided evidence for the wave-particle duality of light?

Accepted Answer

Double slit experiment

Question 4

According to de Broglie, what is the wavelength associated with a particle of mass $$m$$ moving at velocity $$v$$?

Accepted Answer

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

Question 5

Which statement best describes the Bohr model of the atom?

Accepted Answer

Electrons occupy quantized energy levels and emit photons when transitioning between levels.

Question 6

In the photoelectric effect, which factor determines the maximum kinetic energy of emitted electrons?

Accepted Answer

The frequency of the incident light

Question 7

Which equation represents the Heisenberg Uncertainty Principle for position and momentum?

Accepted Answer

$$\Delta x \Delta p \geq \frac{h}{4\pi}$$

Question 8

Which principle explains why no two electrons in an atom can have the same set of quantum numbers?

Accepted Answer

Pauli Exclusion Principle

Question 9

A radioactive isotope has a half-life of 10 years. How much of a 100 g sample remains after 30 years?

Accepted Answer

12.5 g

Question 10

Which type of radioactive decay results in the emission of a helium nucleus?

Accepted Answer

Alpha decay

Question 11

What is the binding energy of a nucleus?

Accepted Answer

The energy required to break the nucleus into its constituent protons and neutrons.

Question 12

Which equation gives the Q-value for a nuclear reaction?

Accepted Answer

$$Q = (m_{initial} - m_{final})c^2$

Question 13

In the double slit experiment with electrons, what is observed on the screen?

Accepted Answer

An interference pattern similar to that of light

Question 14

Which of the following is conserved in all types of radioactive decay?

Accepted Answer

Nucleon number

Question 15

A hydrogen atom's electron transitions from $$n=3 to$$ $$n=2. $$What happens?

Accepted Answer

A photon is emitted with energy equal to the difference between the two levels.

Question 16

Which of the following best describes the strong nuclear force?

Accepted Answer

It binds protons and neutrons together in the nucleus.

Question 17

If the uncertainty in the position of an electron is $$1 	imes 10$$^{-10}$$\ 	ext{m}$$, what is the minimum uncertainty in its momentum?

Accepted Answer

$$\Delta p \geq \frac{h}{4\pi \Delta x} = \frac{6.626 	imes 10$$^{-34}$$}{4\pi 	imes 1 	imes 10$$^{-10}$$} \approx 5.28 	imes 10$$^{-25}$$\ 	ext{kg}\cdot	ext{m/s}$$

Question 18

Which quantum mechanical concept explains the stability of the hydrogen atom?

Accepted Answer

Electrons occupy quantized energy levels described by wave functions.

Question 19

Which of the following is NOT a consequence of the photoelectric effect?

Accepted Answer

The intensity of light determines the maximum kinetic energy of electrons.

Question 20

A nucleus undergoes beta decay. What happens to its atomic number and mass number?

Accepted Answer

Atomic number increases by 1, mass number remains unchanged.

Modern Physics: Quantum Theory, Atomic Structure, and Nuclear Physics

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