Question

Question 2.49 Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nano second range. If the radiation source has the duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 10^15, calculate the energy of the source.

Class XI Structure of Atom Page 68

Answer 1

$frequency ( v ) = \frac{1}{time\: period}$
here,
time period ( T ) = 2 ns = 2 × 10^-9 s
$\therefore\: frequency=\frac{1}{2\times\:10^{-9}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.5 \times {10}^{ 9}Hz$

now, energy of the source = energy of one photons × number of photos produced
= hv × N

here,
N = 2.5 × 10^15
h = 6.626 × 10^-34 Js
v = 0.5 × 10^9 Hz

now,
$E_{source}=hv\times\:N\\\\=6.626\times\:10^{-34}\times\:0.5\times\:10^9\times\:2.5\times\:10^{15}\\\\=8.28\times\:10^{-10}J$