A black body is at a temperature of 5780 text | vedclass

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

Question

(A) According to Wien's displacement law, the wavelength $\lambda_m$ at which the spectral emissive power of a black body is maximum is given by $\lam

Vedclass · Accepted Answer

$U_1  U_3$

Vedclass · Answer

(A) According to Wien's displacement law, the wavelength $\lambda_m$ at which the spectral emissive power of a black body is maximum is given by $\lambda_m = \frac{b}{T}$.Given $b = 2.89 	imes 10^6 	ext{ nm K}$ and $T = 5780 	ext{ K}$.$\lambda_m = \frac{2.89 	imes 10^6}{5780} \approx 500 	ext{ nm}$.Since the peak emission occurs at $\lambda_m = 500 	ext{ nm}$, the energy density $U_2$ at $500 	ext{ nm}$ is the maximum.For wavelengths smaller than $\lambda_m$ $(300 	ext{ nm})$ and larger than $\lambda_m$ $(900 	ext{ nm})$, the energy density is lower than the peak value.Thus, $U_2$ is the maximum, and comparing $U_1$ and $U_3$, the curve for black body radiation is steeper on the shorter wavelength side.Therefore, $U_1  U_3$.

$A$ black body is at a temperature of $5780 \text{ K}$. The energy of radiation emitted by the body at wavelength $300 \text{ nm}$ is $U_1$, at wavelength $500 \text{ nm}$ is $U_2$, and at wavelength $900 \text{ nm}$ is $U_3$. Wien's constant $b = 2.89 \times 10^6 \text{ nm K}$. This shows that:

Similar Questions

$A$ black body emits radiation with maximum intensity at a wavelength of $5000 \mathring{A}$ at a temperature of $1227^\circ C$. If its temperature is increased by $1000^\circ C$, the new wavelength of maximum intensity will be ...... $\mathring{A}$.

$A$ black body at $200 K$ is found to emit maximum energy at a wavelength of $14 \mu m$. When its temperature is raised to $1000 K$,the wavelength at which maximum energy is emitted is:

$A$ particular star (assuming it as a black body) has a surface temperature of about $5 \times 10^4 \ K$. The wavelength in nanometers at which its radiation becomes maximum is $(b = 0.0029 \ mK)$.

Experimental investigations show that the intensity of solar radiation is maximum for a wavelength $480 \, nm$ in the visible region. Estimate the surface temperature of the sun. Given Wien's constant $b = 2.88 \times 10^{-3} \, mK$.

$A$ black body radiates maximum energy at wavelength $\lambda$ and its emissive power is $E$. Now,due to a change in the temperature of that body,it radiates maximum energy at wavelength $\frac{2 \lambda}{3}$. At that temperature,the emissive power is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module