Question

A $500W$ power source emits UV light having a wavelength of $2000\stackrel{\circ }{A}$. How many photons are emitted per minute by the source?

• A. $8.0\times {10}^{23}$
• B. $5.6\times {10}^{24}$
• C. $3.0\times {10}^{22}$
• D. $8.0\times {10}^{20}$

Answer 1

The correct option is C $3.0\times {10}^{22}$

We know,
Energy given out by the source per unit time = Power (P)
Therefore, energy given by the source in 't' sec = $P\times t$
Again, the energy of each photon of green light is given by $=hv=\frac{hc}{\lambda }$
The number of photons (n) emitted in time 't' sec is given by, $n=\frac{P\times t}{\left(\frac{hc}{\lambda }\right)}=\frac{P\times t\times \lambda }{hc}$
Given,
$P=500W=500J/s$,
$t=60s$
Hence,
Number of photons $\left(n\right)=\frac{500\times 60\times 2000\times {10}^{-10}}{6.626\times {10}^{-34}\times 3\times {10}^8}=3.0\times {10}^{22}$