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Question

An ideal black body emits maximum intensity of radiation of wavelength $$5000 \dot{A}$$ at temperature $$1227^oC$$. If its temperature is increased by $${10^3}\space ^oC$$ then the maximum emission wavelength will be:


A
5000˙A
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B
4000˙A
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C
3500˙A
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D
3000˙A
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Solution

The correct option is D $$ 3000 \dot{A}$$
According to Wein's displacement law:
$$\lambda T = b = constant$$
$$T_{1} = 1500K$$
$$\lambda_{1} = 5000\dot{A}  $$
Given that temperature increases by $$1000^{\circ}C$$
$$T_{2} = 2500K$$
$$\lambda_{1} T_{1} = \lambda_{2} T_{2}$$
$$\lambda_{2} = \dfrac{T_{1}}{T_{2}} \lambda_{1} = \dfrac{1500}{2500} \times  5000 = 3000\dot{A} $$

Physics

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