Question

A black body has maximum wavelength ‘λ’ at 2000K. Its corresponding wave length at 3000K will be:
1. 2λ/3
2. 3λ/2
3. 81/16λ
4. 16/81λ

Answer 1

Correct Answer - Option 1 : 2λ/3

Concept:

Wein's law: 

• It states that the blackbody radiation curve for different temperatures peaks at a wavelength is inversely proportional to the temperature.
• ​It is also known as Wien’s displacement law,
• It is named after Wilhelm Wien was derived in the year 1893.

Mathematical representation of the law:

\(λ_{max} = \frac{b}{T}\)

where,
b is the Wien’s displacement constant = 2.8977 × 103 m.K

T is the temperature in kelvins

In other words, we can say that

λ_max . T = Constant

or

\(\frac{λ_1}{λ_2} = \frac{T_2}{T_1}\)-- (1)

Calculation:

Given maximum wavelength at T₁ = 2000 K  ( λ ₁ ) = λ 

We have to find wavelength at T₂ = 3000 K ( λ ₂ ) = ?

Putting these in Equation (1)

\(λ_2 = \frac{λ}{3000}2000\)

⇒ λ 2 = 2 λ /3 

So, the correct option is 2 λ /3 

Applications of weins law:

1. Incandescent bulb light: With the decrease in temperature of the filament, wavelengths are longer making light appear redder
2. The temperature of the sun: One can study the peak emission per nanometres of the sun with a wavelength of 500 nm in the green spectrum which is in the human eye sensitive range.