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

Answer:

(a)

$\lambda _{m}=9.332 \times 10^{-6}m$

(b)

$\lambda _{m}=1.632 \times 10^{-6}m$

(c) $\lambda _{m}=4.988 \times 10^{-7}m$

 

Explanation:

According to the Wein's displacement law

$\lambda _{m}\times T = b$

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

$\lambda _{m}=\frac{b}{T}$

$\lambda _{m}=\frac{2.893\times 10^{-3}}{310}$

$\lambda _{m}=9.332 \times 10^{-6}m$

(b) T = 1500°C = 1500 + 273 = 1773 K

$\lambda _{m}=\frac{b}{T}$

$\lambda _{m}=\frac{2.893\times 10^{-3}}{1773}$

$\lambda _{m}=1.632 \times 10^{-6}m$

(c) T = 5800 K

$\lambda _{m}=\frac{b}{T}$

$\lambda _{m}=\frac{2.893\times 10^{-3}}{5800}$

$\lambda _{m}=4.988 \times 10^{-7}m$