Question

hat are the wavelengths of peak intensity and the corresponding spectral regions for radiating objects at (a) normal human body temperature of 37°C, (b) the temperature of the filament in an incandescent lamp, 1500°C, and (c) the temperature of the surface of the sun, 5800 K?

Answer 1

(a)

`\lambda _(m)=9.332 * 10^(-6)m`

(b)

`\lambda _(m)=1.632 * 10^(-6)m`

(c)
`\lambda _(m)=4.988 * 10^(-7)m`

Step-by-step explanation:

According to the Wein's displacement law

`\lambda _(m)* T = b`

Where, T be the absolute temperature and b is the Wein's displacement constant.

b = 2.898 x 10^-3 m-K

(a) T = 37°C = 37 + 273 = 310 K

`\lambda _(m)=(b)/(T)`

`\lambda _(m)=(2.893* 10^(-3))/(310)`

`\lambda _(m)=9.332 * 10^(-6)m`

(b) T = 1500°C = 1500 + 273 = 1773 K

`\lambda _(m)=(b)/(T)`

`\lambda _(m)=(2.893* 10^(-3))/(1773)`

`\lambda _(m)=1.632 * 10^(-6)m`

(c) T = 5800 K

`\lambda _(m)=(b)/(T)`

`\lambda _(m)=(2.893* 10^(-3))/(5800)`

`\lambda _(m)=4.988 * 10^(-7)m`