Q: According to Wien's displacement law, the wavelength at which the intensity of blackbody radiation is maximum ($$\lambda_{max}) is $$related to the temperature ($$T) by$$:

$$\lambda_{max} T = 2.898 \times 10$$^{-3}$$ \ \mathrm{m \cdot K}$$

Question 1

Which of the following best describes blackbody radiation?

Accepted Answer

Radiation emitted by a perfect absorber and emitter of energy at all wavelengths.

Question 2

According to Wien's displacement law, the wavelength at which the intensity of blackbody radiation is maximum ($$\lambda_{max}) is $$related to the temperature ($$T) by$$:

Accepted Answer

$$\lambda_{max} T = 2.898 	imes 10$$^{-3}$$ \ \mathrm{m \cdot K}$$

Question 3

Planck's quantum hypothesis was necessary to explain which phenomenon?

Accepted Answer

The ultraviolet catastrophe in blackbody radiation.

Question 4

Which equation gives the energy of a photon?

Accepted Answer

$$E = h 
u$$

Question 5

In the photoelectric effect, what happens if the frequency of incident light is below the threshold frequency?

Accepted Answer

No electrons are emitted, regardless of the light's intensity.

Question 6

Which of the following statements about the photoelectric effect is correct?

Accepted Answer

The kinetic energy of emitted electrons depends on the frequency of the incident light.

Question 7

The Compton effect demonstrates that:

Accepted Answer

Photons have momentum and can transfer it to electrons during collisions.

Question 8

According to de Broglie's hypothesis, the wavelength associated with a particle of mass $$m$$ and velocity $$v is$$:

Accepted Answer

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

Question 9

Which of the following best describes Heisenberg's uncertainty principle?

Accepted Answer

It is impossible to simultaneously know both the exact position and momentum of a particle.

Question 10

For a particle in a one-dimensional box of length $$L$$, the allowed energy levels are given by:

Accepted Answer

$$E_n = \frac{n^2$ h^2$}{8mL^2$}$$

Question 11

If the length of a one-dimensional box is doubled, what happens to the energy level separation of an electron in the box?

Accepted Answer

The energy levels move closer together.

Question 12

Which of the following is a direct consequence of the wave-particle duality of matter?

Accepted Answer

Particles such as electrons can exhibit interference patterns.

Question 13

The probability of finding a quantum particle at a given position $$x is $$given by:

Accepted Answer

$$|\Psi(x)|^2$$

Question 14

Which of the following best describes the boundary conditions for a particle in a box of length $$L$$?

Accepted Answer

$$\Psi(0) = 0$$ and $$\Psi(L) = 0$$

Question 15

In the Compton effect, the change in wavelength $$\Delta \lambda of $$the scattered photon is given by:

Accepted Answer

$$\Delta \lambda = \frac{h}{m_e c}(1 - \cos 	heta)$$

Question 16

Which of the following statements about the Schrödinger equation is correct?

Accepted Answer

It describes how the quantum state of a physical system changes with time.

Question 17

If an electron is accelerated from rest through a potential difference $$V$$, its de Broglie wavelength is:

Accepted Answer

$$\lambda = \frac{h}{\sqrt{2meV}}$$

Question 18

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

Accepted Answer

The stopping potential increases with the intensity of the incident light.

Question 19

For a particle in a box, the quantum number $$n$$ determines:

Accepted Answer

The energy level of the particle.

Quantum Physics: Blackbody Radiation, Photoelectric Effect, and Wave-Particle Duality (Chapters 38-40)

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