Two bulb $^{'} A^{'}$ and $^{'} B^{'}$ emit red light and yellow light at $8000 \circ A$ and $4000 \circ A$ respectively. The number of photons emitted by both the bulbs per second in the same. If the rod bulb is labelleld as $100 w a t t s$ , find the wattage of the yellow bulb.

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Solution

$\begin{matrix} P o w e r = 100 w a t t s = \frac{W o r k d o n e}{T i m e} = \frac{E n e r g y U s e d}{T i m e} E = \frac{h c}{λ} \Rightarrow \frac{h c}{\frac{λ}{T i m e}} = 100 w a t t s \frac{P_{A}}{P_{B}} = \frac{\frac{h c}{λ_{A}}}{\frac{T}{\frac{h c}{\frac{λ_{B}}{T}}}} \Rightarrow \frac{\frac{h c}{λ_{A} T}}{\frac{h c}{λ_{B} T}} \Rightarrow \frac{h c}{λ_{A} T} \times \begin{matrix} λ_{B} T h c \end{matrix} \Rightarrow \frac{4000 A^{-}}{8000 A^{-}} \Rightarrow \frac{1}{2} \frac{p_{A}}{P_{B}} = \frac{1}{2}; P_{B} = 2 P_{A} = 200 w a t t s \end{matrix}$

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Two bulb ′A′ and ′B′ emit red light and yellow light at 8000∘A and 4000∘A respectively. The number of photons emitted by both the bulbs per second in the same. If the rod bulb is labelleld as 100watts, find the wattage of the yellow bulb.

Power=100watts=WorkdoneTime=EnergyUsedTimeE=hcλ⇒hcλTime=100wattsPAPB=hcλAThcλBT⇒hcλAThcλBT⇒hcλAT×λBThc⇒4000A−8000A−⇒12pAPB=12;PB=2PA=200watts

Two bulb $^{'} A^{'}$ and $^{'} B^{'}$ emit red light and yellow light at $8000 \circ A$ and $4000 \circ A$ respectively. The number of photons emitted by both the bulbs per second in the same. If the rod bulb is labelleld as $100 w a t t s$ , find the wattage of the yellow bulb.