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JEE Advanced Physics Thermal Properties of Matter 2023 JEE Advanced 2023 (Paper 1)

JEE Advanced Physics Question (2023) — Solution

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 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

Options

  1. A. P → 3 ,   Q → 5 ,   R → 2 ,   S → 3
  2. B. P → 3 ,   Q → 2 ,   R → 4 ,   S → 1
  3. C. P → 3 ,   Q → 4 ,   R → 2 ,   S → 1
  4. D. P → 1 ,   Q → 2 ,   R → 5 ,   S → 3

Answer

C. P → 3 ,   Q → 4 ,   R → 2 ,   S → 1

Step-by-step solution

Maximum wavelength for each case: P   2000   K λ m T = b ⇒ λ m = b T = 2 . 9 × 10 - 3 2000 = 1 . 45 × 10 - 6   m = 1450   nm ( Q )   3000   K λ m T = b ⇒ λ m = 2 . 9 × 10 - 3 3000 = 966 . 66   nm ( R )   5000   K λ m T = b ⇒ λ m = 2 . 9 × 10 - 3 5000 = 580   nm ( S )   10000   K λ m T = b ⇒ λ m = 2 . 9 × 10 - 3 10 , 000 = 290   nm Now for List- II : 1   λ t h = h c ϕ = 1 . 24 × 10 - 6 4 = 0 . 31 × 10 - 6   m = 310   nm For  λ ≤ λ th , emission of photoelectrons will take place. Therefore,  S → 1 . 2  Wavelength range visible to human eye ranges from  400   to   700   nm . Therefore,  R → 2 . 3  Width of the central maxima is directly proportional to the wavelength of the light used. Therefore, for maximum width, maximum wavelength is required. Hence,  P → 3 . 4  Power emitted by blackbody is given by,  σ T 1 4 = 1 16 σ T 4 2 ⇒ T 1 = 1 2 T 2 = 3000   K Therefore,  Q → 4 . 5  For imaging bones X -rays are used in the wavelength range of  1 - 10   nm . None of the options in List- I  matches with it.

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Related: Physics — Thermal Properties of Matter · All PYQ Banks