Question

Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm (visible), (b) λmax = 3 cm (microwave region) and (c) λmax = 3 m (FM radio waves) (Take Wien's constant b = 2.897 × 10^-3 m K).

Answer 1

(a) λmax = 700 nm = 700×10^-9 m,

(b) λmax = 3 cm = 3×10^-2 m,

(c) λmax = 3 m

b = 2.897 × 10^-3 m K

(a)

T= b/λmax = (2.897 × 10^-3 )/ (700×10^-9) 

= 4138 K is the required temperature

(b)

T= b/λmax = (2.897 × 10^-3 )/ (3×10^-2) 

= 9.66×10^-2 K is the required temperature

(c)

T= b/λmax = (2.897 × 10^-3 )/ (3) 

= 9.66×10^-4 K is the required temperature