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Chapter 37: Q. 5 (page 1081)

A2.0-cm-diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of 2.0mm.How much power does the sphere radiate? Assumee=1.

Short Answer

Expert verified

The power that sphere radiates is 3.1×10-10Watt

Step by step solution

01

Given Information

We are given that diameter of metal sphere is2.0-cm , infrared wavelength of spectrum is 2.0mm and e=1.

We are asked to find power that the sphere radiates.

02

Simplify

We are given with the diameter of metal sphere , we will find radius of sphere

r=d2=2cm2=1cm

We will convert cm into m ⇒1cm=0.01m

According to Wien 's law ⇒λ=2.9×106(nm.k)T

We can find the value of T from this equation, T=2.90×106(nm.k)2×106nm=1.45K

now power radiated by sphere is given by ,

Power =eσAT4=1×5.67×10-8×4π×0.012×1.454=3.1×10-10Watt

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