Q: Which law describes the wavelength at which the spectral emittance of a blackbody is maximized?

Wien's displacement law: $$\lambda_{max} = \frac{2.90 \times 10$$^{-3}$$ \text{ m K}}{T}$$

Question 1

Which of the following best describes why a hollow box with a small aperture is a good approximation of a perfect blackbody?

Accepted Answer

Light entering the box is eventually absorbed by the walls, making it a nearly perfect absorber.

Question 2

According to the Stefan-Boltzmann law, what is the total power radiated per unit area by a blackbody at temperature $$T$$?

Accepted Answer

$$P = \sigma T^4$

Question 3

The Rayleigh-Jeans law predicted the so-called 'ultraviolet catastrophe.' What was the main issue with this prediction?

Accepted Answer

It predicted infinite total radiated intensity as wavelength approached zero.

Question 4

Planck resolved the ultraviolet catastrophe by proposing that electromagnetic oscillators could only have energies given by which expression?

Accepted Answer

$$E = nhf$$, where $$n = 0, 1, 2, ...$$

Question 5

Which law describes the wavelength at which the spectral emittance of a blackbody is maximized?

Accepted Answer

Wien's displacement law: $$\lambda_{max} = \frac{2.90 	imes 10$$^{-3}$$ 	ext{ m K}}{T}$$

Question 6

If the temperature of a blackbody increases from 2000 K to 4000 K, by what factor does the total radiated intensity increase?

Accepted Answer

16

Question 7

Which of the following statements about blackbody radiation is correct?

Accepted Answer

A blackbody emits a continuous spectrum of wavelengths.

Question 8

The Heisenberg uncertainty principle for position and momentum is given by:

Accepted Answer

$$\Delta x \Delta p_x \geq \hbar / 2$$

Question 9

In the double-slit experiment with electrons, what is observed if electrons are sent one at a time through the slits?

Accepted Answer

An interference pattern gradually builds up over time.

Question 10

According to the energy-time uncertainty principle, what happens to the uncertainty in energy $$\Delta E if $$the lifetime $$\Delta t of a $$state is very short?

Accepted Answer

$$\Delta E is $$very large.

Question 11

Which of the following is a direct consequence of the quantization of energy in Planck's model?

Accepted Answer

High-frequency oscillators are less effective at emitting radiation at low temperatures.

Question 12

The Planck radiation law for the spectral intensity $$I(\lambda) is$$:

Accepted Answer

$$I(\lambda) = \frac{2\pi hc^2$}{\$$lambda^5$$} \frac{1}{e$$^{hc/\lambda kT}$$ - 1}$$

Question 13

Which experiment directly demonstrates the wave-particle duality of matter?

Accepted Answer

The double-slit experiment with electrons.

Question 14

If a blackbody's temperature is doubled, what happens to the wavelength at which its spectral emittance is maximized?

Accepted Answer

It is halved.

Question 15

Which of the following best explains why the Bohr model cannot be a complete description of the electron in an atom?

Accepted Answer

It violates the Heisenberg uncertainty principle for position and momentum.

Question 16

A star's surface temperature increases from 4000 K to 5800 K. According to the Stefan-Boltzmann law, what is the ratio of the intensities emitted from these two regions?

Accepted Answer

$$\left(\frac{5800}{4000}\$$right)^4$$

Question 17

Which of the following is NOT a characteristic of blackbody radiation?

Accepted Answer

It emits only at discrete wavelengths.

Question 18

What is the physical significance of the Planck constant $$h in $$blackbody radiation?

Accepted Answer

It sets the scale for quantization of energy in electromagnetic oscillators.

Blackbody Radiation, Quantization, and the Uncertainty Principle

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