Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as 2.9 × 10^{-3} {m}-{K} and \; h c/e = 1.24 × 10^{-6} {V}-{m} ] List-I List-II (P) 2000 {K} (1) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work (Q) 3000 {K} (2) The radiation at peak wavelength is visible to human eye. (R) 5000 {K} (3) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction. (S) 10000 {K} (4) The power emitted per unit area is 1/16 of that emitted by a blackbody at temperature 6000 {K}. (5) The radiation at peak emission wavelength can be used to image human bones. [JEE Adv 2023 P1]

Question

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as 2.9 × 10^{-3} {m}-{K} and \; h c/e = 1.24 × 10^{-6} {V}-{m} ]  List-I  List-II  (P) 2000 {K}  (1) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work  (Q) 3000 {K}  (2) The radiation at peak wavelength is visible to human eye.  (R) 5000 {K}  (3) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction.  (S) 10000 {K}  (4) The power emitted per unit area is 1/16 of that emitted by a blackbody at temperature 6000 {K}.    (5) The radiation at peak emission wavelength can be used to image human bones. [JEE Adv 2023 P1]

Examsnet · Accepted Answer

Correct Answer is : P→3,Q→4,R→2,S→1P arrow 3, Q arrow 4, R arrow 2, S arrow 1P→3,Q→4,R→2,S→1

List-I	List-II
(P) $2000 \text{K}$	$\lambda_m T = b$ $\lambda_m = \frac{b}{T} = \frac{2.9 \times 10^{-3}}{2000} = 1.45 \times 10^{-6} \text{m} = 1450 \text{nm}$
(Q) $3000 \text{K}$	$\lambda_m T = b \Rightarrow \lambda_m = \frac{2.9 \times 10^{-3}}{3000} = 966.66 \text{nm}$
(R) $5000 \text{K}$	$\lambda_m T = b \Rightarrow \lambda_m = \frac{2.9 \times 10^{-3}}{5000} = 580 \text{nm}$
(S) $10000 \text{K}$	$\lambda_m T = b \Rightarrow \lambda_m = \frac{2.9 \times 10^{-3}}{10,000} = 290 \text{nm}$

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

JEE Advanced 2023 Paper 1 Solutions