Question

A black body has its cavity in the shape of a cube. Determine the number of modes of vibration per unit volume in the wave length region 4990 angstorm to 5010 angstorm

Answer 1

• Modes of vibration per unit volume in the wavelength region of 4990 A- 5010 A is 8.038 × 10¹⁷ / m³.
• Number of modes of vibration per unit volume can be calculated by using the given formula-

N = 8 π v² dv / c³

And we know that v= c/λ which means dv= - dλ/λ² .

By putting the data we get-

4990 + 5010 /2 = 5000 A⁰

So, dλ = 5010 -4990 = 20 A⁰

By putting the values we get-

N = 8π dλ / λ⁴ = 8.038 × 10¹⁷ / m³

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