Q: A laser emits light with a wavelength of $$400 \ \mathrm{nm}. $$What is the momentum of each photon? (Use $$h = 6.63 \times 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$c = 3.00 \times 10^8$ \ \mathrm{m/s})$$

$$p = \dfrac{h}{\lambda} = 1.66 \times 10$$^{-27}$$ \ \mathrm{kg \cdot m/s}$$

Question 1

Which experiment provided direct evidence for the particle-like properties of light by demonstrating that light can eject electrons from a metal surface?

Accepted Answer

The photoelectric effect experiment

Question 2

According to Einstein’s explanation of the photoelectric effect, what is the minimum energy required to remove an electron from a metal surface called?

Accepted Answer

Work function

Question 3

A photon has a wavelength of $$\lambda = 500 \ \mathrm{nm}. $$What is its energy in electron volts ($$\mathrm{eV}$$)? (Use $$h = 6.63 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$c = 3.00 	imes 10^8$ \ \mathrm{m/s}$$, $$1 \ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$ \ \mathrm{J})$$

Accepted Answer

$$E = \dfrac{hc}{\lambda} = 2.48 \ \mathrm{eV}$$

Question 4

Which of the following best describes the Compton effect?

Accepted Answer

The increase in wavelength of X-rays scattered by electrons, demonstrating the particle nature of light

Question 5

The de Broglie wavelength of an electron with momentum $$p is $$given by:

Accepted Answer

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

Question 6

Which experiment demonstrated the wave-like nature of electrons by showing diffraction patterns?

Accepted Answer

The Davisson-Germer experiment

Question 7

According to the Bohr model, the allowed energy levels of the hydrogen atom are given by:

Accepted Answer

$$E_n = -\dfrac{13.6 \ \mathrm{eV}}{n^2$}$$

Question 8

Which of the following statements about the Heisenberg Uncertainty Principle is correct?

Accepted Answer

It limits the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known.

Question 9

A particle is confined in a one-dimensional infinite potential well of width $$L. $$What is the energy of the ground state ($$n=1$$)?

Accepted Answer

$$E_1$$ = \dfrac{$$h^2$$}{$$8mL^2$$}$$

Question 10

Which quantum number determines the shape of an electron’s orbital in the hydrogen atom?

Accepted Answer

Azimuthal (angular momentum) quantum number $$l$$

Question 11

Which phenomenon provides evidence that electrons possess intrinsic angular momentum (spin)?

Accepted Answer

The splitting of spectral lines in a magnetic field

Question 12

What is the physical significance of the wavefunction $$\psi(x) in $$quantum mechanics?

Accepted Answer

Its square modulus $$|\psi(x)|^2$$ gives the probability density of finding a particle at position $$x.$$

Question 13

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

Accepted Answer

Pauli Exclusion Principle

Question 14

A laser emits light with a wavelength of $$400 \ \mathrm{nm}. $$What is the momentum of each photon? (Use $$h = 6.63 	imes 10$$^{-34}$$ \ \mathrm{J \cdot s}$$, $$c = 3.00 	imes 10^8$ \ \mathrm{m/s})$$

Accepted Answer

$$p = \dfrac{h}{\lambda} = 1.66 	imes 10$$^{-27}$$ \ \mathrm{kg \cdot m/s}$$

Question 15

Which of the following best describes quantum tunneling?

Accepted Answer

A particle passing through a potential barrier even when its energy is less than the barrier height

Question 16

Which law describes the total power radiated per unit area of a blackbody in terms of its temperature?

Accepted Answer

Stefan-Boltzmann Law: $$P = \sigma T^4$

Question 17

In the context of atomic spectra, what does the observation of discrete emission lines indicate?

Accepted Answer

Atoms have quantized energy levels.

Question 18

Which experiment led to the nuclear model of the atom by showing that most alpha particles passed through gold foil with little deflection?

Accepted Answer

Rutherford scattering experiment

Question 19

Which of the following is a consequence of the quantization of angular momentum in the Bohr model?

Accepted Answer

Electrons can only occupy certain allowed orbits with specific energies.

Question 20

Which of the following best describes the outcome of the double-slit experiment with electrons?

Accepted Answer

Electrons exhibit both wave-like and particle-like properties.

Quantum Physics: Photons, Wave-Particle Duality, Quantum Mechanics, and Atomic Structure

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