Question

Match the temperature of a black body given in L-I with an appropriate statement in L-II and choose the correct option. (given: wien is constant as $2.9\times10^{-3}$ m.k. $\frac{hc}{e}=1.24\times10^{-6}\,v.m$

| ** List-I**| | **List-II **
---|---|---|---
(P)| 2000 K| (1)| The radiation at peek wavelength can lead to the emission of photo e$^-$ from a metal of work function 4 eV
(Q)| 3000 K| (2)| The radiation at peek wavelength is visible to the human eye
(R)| 5000K| (3)| The radiation at peek emission wavelength will result in the widest central maximum of a single slit diffraction
(S)| 10000K| (4)| The power emitted per unit area is $\frac{1}{16}$ of that emitted by a black body at a temperature of 6000K.
| | (5)| The radiation at peak emission wavelength can be used to image human bone.

Answer 1

The correct answer is : P$\rightarrow$3; Q$\rightarrow$4; R$\rightarrow$2; S$\rightarrow$1
$\lambda\times T=b$
$\lambda=\frac{b}{T}$
$E=\frac{hc}{\lambda}=\frac{hcT}{b}$
$E=(\frac{hc}{eb})\times T\,eb$
$E=\frac{1.24\times10^{-6}}{2.9\times10^{-3}}\times T\,ev$
$E=(0.428\times 10^{-3}\times T)\,\,eV$
(P) T = 2000K $\Rightarrow$ E = 0.856eV
(Q) T = 3000K $\Rightarrow$ E = 1.284eV
(R) T = 5000K $\Rightarrow$ E=2.14eV
(S) T = 10000K $\Rightarrow$ E=4.28eV