Question

Find the wavelength at which a black body radiates maximum energy, if it's temperature is 427 c

Answer 1

Answer:$\lambda_{max} = 4.14\ micrometer$

Explanation:

Given that,

Temperature $T = 427+273 = 700 K$

Using Wien's displacement law

$\lambda_{max} = \dfrac{b}{T}$

Where,

b = Wien's displacement constant

T = temperature

Now, the wave length

$\lambda _{max} = \dfrac{2.898\times10^{-3}\ mK}{700\ K}$

$\lambda_{max} = 0.414\times10^{-5}\ m$

$\lambda_{max} = 4.14\ micrometer$

Hence, this is the required solution.

Answer 2

Answer:

4.14×10  

−6

m

Explanation:

 

Temperature at which maximum energy is radiated T=427  

o

C

∴ T=427+273=700K

From Wein's displacement law, wavelength λ  

max

​

=  

T

b

​

 

∴ λ  

max

​

=  

700

(2.898×10  

−3

)

​

 

⟹ λ  

max

​

=4.14×10  

−6

 m