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Chapter 6: Q38E (page 1315)

Determine λm, the wavelength at the peak of the Planck distribution, and the corresponding frequency f, at these temperatures: (a) 3.00 K; (b) 300 K; (c)3000 K.

Short Answer

Expert verified
  1. λm=9.67×10-4;f=3.10×1011Hz
  2. λm=9.67×10-6;f=3.10×1013Hz
  3. λm=9.67×10-7;f=3.10×1014Hz

Step by step solution

01

Determine the wavelength and frequency at t = 3.00 K

Use Wien displacement law to find the wavelength

And, the relation between the wavelength and the frequency of a photon is


a. At T = 3.00 K,

The wavelength is

And, frequency is

Therefore, at t = 3.00 K the wavelength at the peak of the Planck’s distribution is and the corresponding frequency is.

02

Determine the wavelength and frequency at t = 300 K   

b. Substitute the values in the equation found

And, frequency is


Therefore, at t = 300 K the wavelength at the peak of the Planck distribution is and the corresponding frequency is

03

Determine the wavelength and frequency at t = 3000 K

c. Substitute the values in the equation found


And, frequency is


Therefore, at t = 3000 K the wavelength at the peak of the Planck distribution is , and the corresponding frequency is.

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