Lifetimes of the molecules in the excited states are often measured

Question.

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 $2 \mathrm{~ns}$ and the number of photons emitted during the pulse source is $2.5 \times$ $10^{15}$, calculate the energy of the source.


Solution:

Frequency of radiation (v),

$v=\frac{1}{2.0 \times 10^{-9} \mathrm{~s}}$

$v=5.0 \times 10^{8} \mathrm{~s}^{-1}$

Energy $(E)$ of source $=N h v$

Where,

$N=$ number of photons emitted

$h=$ Planck's constant $v=$

frequency of radiation

Substituting the values in the given expression of $(E):$

$E=\left(2.5 \times 10^{15}\right)\left(6.626 \times 10^{-34} \mathrm{Js}\right)\left(5.0 \times 10^{8} \mathrm{~s}^{-1}\right)$

$\left.E=8.282 \times 10^{-10}\right]$

Hence, the energy of the source $(E)$ is $8.282 \times 10^{-10} \mathrm{~J}$.

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