Question

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

• A. $n_{R}=n_{V}$
• B. $n_{R}>n_{V}$
• C. $n_{R} < n_{V}$
• D. $n_{R}\leq n_{V}$

Answer 1

Answer: (B)

Energy possessed by a photon is given by
$E=hf=\frac{h c}{\lambda }$
If power of each bulb is $P$ then energy given out in $time t$ equal to $Pt.$ Let the number of photons be $n$ , then
$n=\frac{P t}{E}=\frac{P t}{\left(\right. h c / \lambda \left.\right)}=\frac{P t \lambda }{h c}$
For red light, $n_{R}=\frac{P t \lambda _{R}}{h c}$
For violet light, $n_{V}=\frac{P t \lambda _{V}}{h c}$
$∴ \, \, \, \frac{n_{R}}{n_{V}}=\frac{\lambda _{R}}{\lambda _{V}}$
As $\lambda _{R}>\lambda _{V}$
So, $n_{R}>n_{V}$