Question

A certain laser transition emits $6.37\times {10}^{15}$ quanta per second per square meter. The power output in joules per square meter per second would be:
(Given : $\lambda =632.8\text{nm}$)

• A. $5\times {10}^{-5}{\text{J m}}^{-2}{\text{sec}}^{-1}$
• B. $2\times {10}^{-3}{\text{J m}}^{-2}{\text{sec}}^{-1}$
• C. $9.2\times {10}^{-3}{\text{J m}}^{-2}{\text{sec}}^{-1}$
• D. None of the above

Answer 1

The correct option is B $2\times {10}^{-3}{\text{J m}}^{-2}{\text{sec}}^{-1}$

We know that,

$1$ photon has energy, $E=h\nu$
$n$ photons will have energy,$E=nh\nu$
Given:
$n=6.37\times {10}^{15}$ ${\text{photons m}}^{-2}{\text{sec}}^{-1}$
$\lambda =632.8\text{nm}=6.32\times {10}^{-7}\text{m}$

Since we have to calculate power in ${\text{J m}}^{-2}{\text{sec}}^{-1}$ and n is given in:
$\text{photons}$ ${\text{m}}^{-2}{\text{sec}}^{-1}$, we can write,
$P=nh\nu =nh\frac{c}{\lambda }$

We know that,
$c=3\times {10}^8\text{m/s}$
$h=6.63\times {10}^{-34}\text{J s}$
Putting the values, we get
$P=2\times {10}^{-3}{\text{J m}}^{-2}{\text{sec}}^{-1}$