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 $2.9 \times 10^{-3} \mathrm{~m}-\mathrm{K}$ and $\frac{\mathrm{hc}}{\mathrm{e}}=1.24 \times 10^{-6} \mathrm{~V}-\mathrm{m}$] | List-I | | List-II | | |---|---|---|---| | (P) | 2000 K | (1) | The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function 4 eV | | (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. |

(C) $P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 1$

(A) $P \rightarrow 3, Q \rightarrow 5, R \rightarrow 2, S \rightarrow 3$

(B) $P \rightarrow 3, Q \rightarrow 2, R \rightarrow 4, S \rightarrow 1$

(D) $P \rightarrow 1, Q \rightarrow 2, R \rightarrow 5, S \rightarrow 3$

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Heat & Thermodynamics

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 \times 1 0^{- 3} m - K

and

\frac{hc}{e} = 1.24 \times 1 0^{- 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 function 4 eV
(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.

(A) $P \to 3, Q \to 5, R \to 2, S \to 3$
(B) $P \to 3, Q \to 2, R \to 4, S \to 1$
(C) $P \to 3, Q \to 4, R \to 2, S \to 1$ ✓ Correct
(D) $P \to 1, Q \to 2, R \to 5, S \to 3$

Answer: (C)

Solution

Using Wien's law:

λ_{m} = \frac{b}{T}

where

b = 2.9 \times 1 0^{- 3}

m·K.

(P) T = 2000 K:

λ_{m} = \frac{2.9 \times 1 0 ^{- 3}}{2000} = 1.45 \times 1 0^{- 6}

m = 1450 nm (infrared, longest wavelength) → widest diffraction (3).

(Q) T = 3000 K:

λ_{m} = \frac{2.9 \times 1 0 ^{- 3}}{3000} \approx 967

nm (near-infrared). Power:

P \propto T^{4}

, so

\frac{P _{3000}}{P _{6000}} = (\frac{3000}{6000})^{4} = \frac{1}{16}

→ (4).

(R) T = 5000 K:

λ_{m} = \frac{2.9 \times 1 0 ^{- 3}}{5000} = 580

nm (yellow, visible) → (2).

(S) T = 10000 K:

λ_{m} = \frac{2.9 \times 1 0 ^{- 3}}{10000} = 290

nm (UV). Energy:

E = \frac{h c}{λ} = \frac{1240}{290} \approx 4.3

eV > 4 eV → can cause photoelectric emission → (1).

Answer: (C)

P \to 3, Q \to 4, R \to 2, S \to 1

JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Single correct option

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JEE Advanced · 2023 · 04 Jun 2023 · Paper 1 · Heat & Thermodynamics

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