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Chapter 7: Q 7.37 (page 293)

Prove that the peak of the Planck spectrum is at x = 2.82.

Short Answer

Expert verified

Hence proved that plank's spectrum is at x = 2.82.

Step by step solution

01

Given information

The peak of the Planck spectrum is at e = 2.82.

02

Explanation

Set the derivative of x3/ex-1with respect to x equals to zero to get the maximum, then solve for:

鈭�鈭�xx3ex-1=03x2ex-1-x3exex-12=03x2ex-1-x3ex=03x2ex-3x2-x3ex=03ex-3-xex=0

Using matlab to solve the above equation: The code is:

Therefore,x=2.8214

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Most popular questions from this chapter

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(a) Write equation 7.121 for this system as a sum over energy levels, taking degeneracy into account. Replace Tand渭with the dimensionless variables t=kT/hfandc=渭/hf.

(b) Program a computer to calculate this sum for any given values of tandc. Show that, for N=2000, equation 7.121 is satisfied at t=15provided that c=-10.534. (Hint: You'll need to include approximately the first 200 energy levels in the sum.)

(c) For the same parameters as in part (b), plot the number of particles in each energy level as a function of energy.

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