JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Atomic Structure

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Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is ____.

A.

T_{4} > T_{3} > T_{2} > T_{1}

B. The black body consists of particles performing simple harmonic motion.
C. The peak of the spectrum shifts to shorter wavelength as temperature increases.
D.

\frac{T _{1}}{v _{1}} = \frac{T _{2}}{v _{2}} = \frac{T _{3}}{v _{3}} \neq =

constant
E. The given spectrum could be explained using quantisation of energy.

Answer: 2

Solution

Reading the curves, the hottest body gives the tallest peak lying at the shortest wavelength, so the temperatures fall as

T_{1} > T_{2} > T_{3} > T_{4}

, and the statement reversing this order is wrong. A black body's emission reflects quantised oscillators rather than the classical vibration of particles, so the simple-harmonic-motion statement is wrong. As temperature rises the peak does shift to shorter wavelength in keeping with Wien's law, so that statement is right. Wien's law

λ_{m a x} T = constant

, rewritten with

ν = c / λ

, makes

T / ν

a constant, so the statement calling that ratio non-constant is wrong. The spectrum was explained only once energy was taken as quantised, so that statement is right. Two of the statements are correct.

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer

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JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Atomic Structure

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