The black body spectrum of an object O_1 is s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to Wien's displacement law,the wavelength $\lambda_{\max}$ at which the radiant intensity is maximum is inversely proportional to the ab

Vedclass · Accepted Answer

$81:1$

Vedclass · Answer

(D) According to Wien's displacement law,the wavelength $\lambda_{\max}$ at which the radiant intensity is maximum is inversely proportional to the absolute temperature $T$ of the black body:$\lambda_{\max} T = b$ (where $b$ is Wien's constant).For object $O_1$: $\lambda_1 = 200\,nm$,so $T_1 = \frac{b}{200}$.For object $O_2$: $\lambda_2 = 600\,nm$,so $T_2 = \frac{b}{600}$.According to the Stefan-Boltzmann law,the power emitted per unit area (emissive power) $E$ is proportional to the fourth power of the absolute temperature:$E \propto T^4$.Therefore,the ratio of power emitted per unit area by $O_1$ to that of $O_2$ is:$\frac{E_1}{E_2} = \left( \frac{T_1}{T_2} \right)^4 = \left( \frac{b/200}{b/600} \right)^4 = \left( \frac{600}{200} \right)^4 = (3)^4 = 81$.Thus,the ratio is $81:1$.

Similar Questions

The energy distribution $E$ with the wavelength $\lambda$ for black body radiation at temperature $T \ K$ is shown in the figure. As the temperature is increased,the maxima will:

The emissive power of a sphere of area $0.04 \,m^2$ is $0.7 \,kcal \,s^{-1} \,m^{-2}$. The amount of heat radiated in $20 \,s$ is: (in $\,kcal$)

If a black wire of platinum is heated, its colour first appears red, then yellow, and finally white. This can be understood on the basis of:

$A$ black body at a temperature of $3000 \ K$ cools down. The wavelength corresponding to maximum energy density shifts by $\Delta \lambda = 9 \ \mu m$. What is the new temperature of the black body (in $K$)? (Given $b = 3 \times 10^{-3} \ m \cdot K$)

The wavelength of maximum emission from a body at a temperature of $200 \, K$ is $14 \, \mu m$. If the temperature of the body is increased to $1000 \, K$,find the new wavelength of maximum emission.

Vedclass Test Series

Exam Paper Generator

Online Exam Module