Question

The wavelength of maximum intensity emitted by a blackbody at temperature 1227°C is 5000 Å. If the temperature is increased then the wavelength of maximum intensity will be
1. 3000 Å
2. 3500 Å
3. 4000 Å
4. 960 Å

Answer 1

Correct Answer - Option 3 : 4000 Å

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,

\(λ_{max} = \frac{b}{T}\)

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

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

Calculation:

Given,

T₁ = 1227^∘C = 1500 K

λ₁ =  5000 Å

From the relation

\(λ_{max} = \frac{b}{T}\)

i.e. the temperature is inversely proportional to wavelength. Therefore, on increasing temperature, the wavelength will decrease.

Hence, from the above options, the wavelength of maximum intensity will be 4000 Å.