If $n_{R}$ and $n_{V}$ denote the number of photons emitted by a red bulb and violet bulb of equal power in a given time, then:

n_{R} = n_{V}

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n_{R} > n_{V}

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n_{R} < n_{V}

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n_{R} \geq n_{V}

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Solution

The correct option is B $n_{R} > n_{V}$
Photons are the packets of energy (or energy particle) which are emitted by a source of radiation.
Energy possessed by a photon is given by
$E = h v = \frac{h c}{λ}$
If power of each photon is P, then energy given out in t second is equal to Pt. Let the number of photons be n, then
$n = \frac{P t}{E} = \frac{P t}{(h c / λ)} = \frac{P t λ}{h c}$
For red light, $n_{R} = \frac{P t λ_{R}}{h c}$
For violet light, $n_{V} = \frac{P t λ_{V}}{h c}$
$∴ \frac{n_{R}}{n_{V}} = \frac{λ_{R}}{λ_{V}}$
As $λ_{R} > λ_{V}$
So, $n_{R} > n_{V}$

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