Question

Lifetimes of the molecules in the excited state 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 $2.5\times {10}^{15}$, calculate the energy of the source.

Answer 1

Given Data: Duration$=2ns=2\times {10}^{-9}$ seconds

Number of emitted photons $=2.5\times {10}^{15}$

Formulas to be used:

Energy $=Nh\omega$

Where N = number of emitted photons during the pulse source

$h=$ Planck’s constant $=6.626\times {10}^{-34}$

$\omega =frequencyoftheradiationsource$

Frequency of source$=\frac{1}{Durationofthesource}$

Calculation:

Step 1: Find frequency of source

$\frac{1}{Durationofthesource}$

$\frac{1}{2\times {10}^{-9}}=0.5\times {10}^9$

Step 2: Substituting

$N=2.5\times {10}^{15}$

$h=6.626\times {10}^{-34}$

$\omega =0.5\times {10}^9$

In the energy formula, we get ,

Energy $=(2.5\times {10}^{15})(6.626\times {10}^{-34})(0.5\times {10}^9)=8.28\times {10}^{-10}$ J