Question

A black body emits radiations of maximum intensity at 5000 $\buildrel _\circ \over {\mathrm{A}}$ when its temperature is 1227 $^\circ$ C. If its temperature increased by 1000 $^\circ$ C then the maximum intensity of emitted radiation will be at:
(A) 2754.8 $\buildrel _\circ \over {\mathrm{A}}$
(B) 3000 $\buildrel _\circ \over {\mathrm{A}}$
(C) 3500 $\buildrel _\circ \over {\mathrm{A}}$
(D) 4000 $\buildrel _\circ \over {\mathrm{A}}$

Answer 1

Hint: A blackbody also known as perfect emitter or perfect absorber, upon being heated, emits radiation of various wavelengths. The product of maximum wavelength that a blackbody emits and the temperature of a blackbody remains constant.
Formula used:
The maximum wavelength of emission for a black body is related to the temperature of the blackbody by Wien's displacement law as:
$\lambda_m = \dfrac{C}{T}$ .

Complete answer:
We are given that when the given body is at a temperature of 1227$^\circ$ C, the wavelength of the light emitted at maximum intensity is 5000 $\buildrel _\circ \over {\mathrm{A}}$. First, we convert the given temperature in Kelvins.
$1227 + 273 = 1500$K
Then, we determine the constant C, by taking the product of wavelength and temperature:
$C = 5000 \times 1500 = 7.5 \times 10^6 \buildrel _\circ \over {\mathrm{A}}K$ .
Now, as the temperature is increased by 1000 $^\circ$ C, the new temperature becomes 2500 K. The wavelength at this temperature becomes:
$\lambda_m = \dfrac{C}{T}$
$\lambda_m = \dfrac{7.5 \times 10^6 \buildrel _\circ \over {\mathrm{A}} K}{2500 K } = 3000 \buildrel _\circ \over {\mathrm{A}}$ .

Therefore, the correct answer is option (B).

Additional Information:
Blackbody radiation forms an important experiment that was extremely crucial in establishing the most impactful branch in physics called Quantum Mechanics. Quantum mechanics is a branch that deals with the study of microscopic objects and improves our understanding in various branches of physics.

Note:
There are various laws given for blackbody radiation but the one that relates the temperature and the wavelength is Wien's law. The emission spectra of the blackbody is obtained in the continuous form. It peaks at certain wavelengths i.e., when a blackbody is at a certain temperature, it emits light of various wavelengths, the energy density is maximum for certain wavelengths (more intense). Therefore, one should note that we are using the relation for the wavelength of maximum intensity and temperature.