If nR and nV denote the number of photons emitted by a red bulb and violet bulb of equal power in a given time, then

Question

If nR and nV denote the number of photons emitted by a red bulb and violet bulb of equal power in a given time, then (A) nR=nV (B) nR>nV (C) nR < nV (D) nR≤ nV

Tardigrade Admin · Accepted Answer

Energy possessed by a photon is given by

E = h f = \frac{h c}{λ}

If power of each bulb is

P

then energy given out in

t im e t

equal to

Pt .

Let the number of photons be

n

, then

n = \frac{Pt}{E} = \frac{Pt}{( h c / λ )} = \frac{Pt λ}{h c}

For red light,

n_{R} = \frac{Pt λ _{R}}{h c}

For violet light,

n_{V} = \frac{Pt λ _{V}}{h c}

∴ \frac{n _{R}}{n _{V}} = \frac{λ _{R}}{λ _{V}}

As

λ_{R} > λ_{V}

So,

n_{R} > n_{V}

Q. 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

$n_{R} = n_{V}$

$n_{R} > n_{V}$

$n_{R} < n_{V}$

$n_{R} \leq n_{V}$

Q. If nR​ and nV​ denote the number of photons emitted by a red bulb and violet bulb of equal power in a given time, then

nR​=nV​

nR​>nV​

nR​<nV​

nR​≤nV​

Q. 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

$n_{R} = n_{V}$

$n_{R} > n_{V}$

$n_{R} < n_{V}$

$n_{R} \leq n_{V}$