Q: Which law describes the wavelength at which the emission of a blackbody spectrum is maximized, and what is its mathematical form?

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

Question 1

Which of the following best explains why a hollow box with a small aperture is used to approximate a perfect blackbody in experiments?

Accepted Answer

Light entering the box is eventually absorbed by multiple reflections, making the box 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 at short wavelengths.

Question 4

Planck resolved the ultraviolet catastrophe by introducing which key idea?

Accepted Answer

Energy is quantized and can only take values $$E = nhf.$$

Question 5

Which law describes the wavelength at which the emission of a blackbody spectrum is maximized, and what is its mathematical form?

Accepted Answer

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

Question 6

A blackbody at 2000 K emits radiation with a peak wavelength at $$\lambda_{max}. If $$the temperature is increased to 4000 K, what happens to $$\lambda_{max}$$?

Accepted Answer

$$\lambda_{max} is $$halved

Question 7

Which of the following is a direct consequence of the Heisenberg uncertainty principle for position and momentum?

Accepted Answer

The product of the uncertainties in position and momentum is always greater than or equal to $$\frac{\hbar}{2}.$$

Question 8

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

Accepted Answer

An interference pattern still forms, demonstrating the wave nature of electrons.

Question 9

Which formula gives the energy of a photon emitted or absorbed during a transition between two energy levels in the Bohr model?

Accepted Answer

$$E = hf$$

Question 10

According to Planck's quantum hypothesis, what is the probability that an oscillator at temperature $$T is in $$its first excited state, given $$hf \gg kT$$?

Accepted Answer

Close to 0

Question 11

Which of the following statements about blackbody radiation is correct?

Accepted Answer

A blackbody emits a continuous spectrum of radiation.

Question 12

The Planck radiation law for the spectral emittance of a blackbody is given by which of the following expressions?

Accepted Answer

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

Question 13

If a system remains in a metastable state for a very short time $$\Delta t$$, what does the Heisenberg uncertainty principle imply about the uncertainty in its energy $$\Delta E$$?

Accepted Answer

$$\Delta E$$ must be very large

Question 14

Which of the following best describes the principle of complementarity in quantum mechanics?

Accepted Answer

Wave and particle models cannot be applied simultaneously to describe a single quantum event.

Question 15

A blackbody at temperature $$T$$ emits radiation with a total intensity $$I. If $$the temperature is doubled, what happens to the total intensity?

Accepted Answer

It increases by a factor of 16

Question 16

Which of the following is a direct application of the energy-time uncertainty principle?

Accepted Answer

The finite width of spectral lines due to short-lived excited states

Question 17

In the context of blackbody radiation, what does the area under the spectral emittance curve represent?

Accepted Answer

The total intensity (power per unit area) emitted by the blackbody

Question 18

Which of the following statements about the Bohr model and the uncertainty principle is correct?

Accepted Answer

The Bohr model violates the uncertainty principle by assuming definite orbits.

Blackbody Radiation, Quantization, and the Uncertainty Principle

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