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Match the temperature of a blackbody listed in Group-I to the corresponding statement in Group-II, and select the correct answer.
[Given: Wien’s constant = 2.9 × 10⁻³ m-K and hc/e = 1.24 × 10⁻⁶ V-m]
Group-I:
(P) 2000 K
(Q) 3000 K
(R) 5000 K
(S) 10000 K
Group-II:
(1) The peak wavelength of emitted radiation can cause photoelectron ejection from a metal with a work function of 4 eV.
(2) The peak wavelength of emitted radiation falls within the visible spectrum.
(3) The peak wavelength of emitted radiation produces the broadest central diffraction maximum in a single-slit setup.
(4) The energy radiated per unit area is one-sixteenth of that emitted by a blackbody at 6000 K.
(5) The peak wavelength of emitted radiation is suitable for imaging human bones.
- P → 1, Q → 2, R → 5, S → 3
- P → 3, Q → 2, R → 4, S → 1
- P → 3, Q → 4, R → 2, S → 1
- P → 3, Q → 5, R → 2, S → 3
Correct answer: P → 3, Q → 4, R → 2, S → 1
Solution
Peak wavelengths are 1450 nm (P, longest -> broadest single-slit central maximum, statement 3), 967 nm (Q, energy/area = (3000/6000)^4 = 1/16, statement 4), 580 nm (R, visible, statement 2) and 290 nm (S, photon 4.28 eV > 4 eV work function, statement 1). So P->3, Q->4, R->2, S->1.
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