Thermal Properties of Matter - Result Question 37

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38. A black body has maximum wavelength $\lambda_m$ at temperature $2000 K$. Its corresponding wavelength at temperature $3000 K$ will be[2001]

======= ####38. A black body has maximum wavelength $\lambda_m$ at temperature $2000 K$. Its corresponding wavelength at temperature $3000 K$ will be[2001]

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/thermal-properties-of-matter/thermal-properties-of-matter—result-question-37.md (a) $\frac{3}{2} \lambda_m$

(b) $\frac{2}{3} \lambda_m$

(c) $\frac{4}{9} \lambda_m$

(d) $\frac{9}{4} \lambda_m$

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Answer:

Correct Answer: 38. (b)

Solution:

  1. (b) According to Wein’s displacement law, $\lambda_m T=2.88 \times 10^{-3}$

When $T=2000 K$,

$\lambda_m(2000)=2.88 \times 10^{-3}$

When $T=3000 K$,

$\lambda_m^{\prime}(3000)=2.88 \times 10^{-3}$

Dividing (1) by (2),

$ \frac{2}{3} \frac{\lambda_m}{\lambda_m^{\prime}}=1 \Rightarrow \frac{\lambda_m}{\lambda_m^{\prime}}=\frac{3}{2} \Rightarrow \lambda_m^{\prime}=\frac{2}{3} \lambda_m $