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In this lesson, we will learn how to relate a blackbody temperature to its emitted and absorbed light wavelengths and how to relate those to photon energies.

Q1:

Determine the power intensity of radiation per unit wavelength emitted at a wavelength of 500.0 nm by a blackbody at a temperature of 1 0 0 0 0 K.

Q2:

A 200-W heater emits a 1.50- 𝜇 m radiation. Radiation from the heater warms a 4.00-kg body by 2.00 K.

What value of the energy quantum does it emit?

Assuming that the specific heat capacity of the body is 0.83 kcal/kg⋅K, how many photons must be absorbed to warm the body?

Assuming that all the radiation that the heater emits is absorbed by the body, how much time is required for the body’s temperature to increase?

Q3:

Lasers can be used as surgical instruments to vaporize flesh by heating it. A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 μm. In 1.00 ms, this laser raised the temperature of 1.00 cm^{3} of flesh to 1 0 0 ∘ C and evaporated it. Flesh has a latent heat of vaporization of 2 2 5 6 kJ/kg.

How many photons were required to vaporize the flesh?

What was the minimum power output during the flash?

Q4:

A photon has the same energy as a proton that is moving at 0 . 0 1 0 0 𝑐 .

What is the wavelength of the photon?

What is the energy of the photon?

What is the kinetic energy of the proton?

Q5:

What is the minimum frequency of a photon required to ionize a L i 2 + ion in its first excited state if the energy required is 30.6 eV? Use a value of 4 . 1 4 × 1 0 eV⋅s for the value of the Planck Constant.

Q6:

The tungsten elements of incandescent light bulbs operate at 700 K. At what frequency does the filament radiate maximum energy?

Q7:

The radiant energy from the Sun reaches its maximum at a wavelength of about 0.5 μm. What is the approximate temperature of the Sun’s surface?

Q8:

The wavelengths of visible light range from approximately 390 nm to 770 nm. What is the corresponding range of photon energies for visible light?

Q9:

Calculate the temperature of the Sun, modeling the Sun as a black body emitting radiation at a maximum intensity at a wavelength of 0.500 micrometres.

Q10:

Calculate the heat flux emitted from the Sun’s surface, modeling the Sun as a black body emitting radiation at maximum intensity at a 0.50-micrometer wavelength.

Q11:

In about five billion years, the Sun will evolve into a red giant. Assume that its surface temperature will decrease to about half its present value of 5 7 7 8 K, while its present radius of 6 . 9 0 0 × 1 0 m will increase to 1 . 5 0 0 × 1 0 m, which is the current Earth-Sun distance. Calculate the ratio of the total power emitted by the Sun in its red giant stage to its present power.

Q12:

Treating the human body as a blackbody, determine the percentage increase in the total power of its radiation when its temperature increases from 9 8 . 8 ∘ F to 1 0 0 ∘ F .

Q13:

The tungsten elements of incandescent light bulbs operate at 700 K. At what frequency does the filament radiate the most energy?

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