Question

A monochromatic beam of electromagnetic radiation has an intensity of $1W/m^2$ . Then the average number of photons per $m^3$ for a 10MeV $\gamma$ ray is ?

• A. 4166
• B. 3000
• C. 5000
• D. 2083

Answer 1

The correct option is D 2083

We know,

$I=\frac{E}{t\times A}$

$I=\frac{nh\nu }{t\times A}$

given,

$h\nu =10\times {10}^6\times 1.6\times {10}^{-19}=1.6\times {10}^{-12}$

Let $l$ be distance travelled in time $t$,

On multiplication with $l$in numerator and denominator

$1=\frac{nl1.6\times {10}^{-12}}{tlA}=\frac{1.6\times {10}^{-12}\times c}{lA}$

$\frac{n}{Al}=\frac{{10}^4}{4.8}=2083$

Option $\text{D}$ is the correct answer