Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has the duration of $2 \, ns$ and the number of photons emitted during the pulse source is $2.5 \times 10^{15}$,calculate the energy of the source.

The energy of a photon is given by $E_{photon} = h\nu$. However,the frequency $\nu$ is related to the duration of the pulse $\Delta t$ as $\nu = \frac{1}{\Delta t}$.
Given:
Duration $\Delta t = 2 \, ns = 2.0 \times 10^{-9} \, s$
Number of photons $N = 2.5 \times 10^{15}$
Planck's constant $h = 6.626 \times 10^{-34} \, J \cdot s$
Frequency $\nu = \frac{1}{2.0 \times 10^{-9} \, s} = 5.0 \times 10^{8} \, s^{-1}$
Total energy $E = N \times h \times \nu$
$E = (2.5 \times 10^{15}) \times (6.626 \times 10^{-34} \, J \cdot s) \times (5.0 \times 10^{8} \, s^{-1})$
$E = 8.2825 \times 10^{-10} \, J$
Thus,the energy of the source is $8.2825 \times 10^{-10} \, J$.