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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 2.5×1015, calculate the energy of the source.

Solution
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Given Data: Duration=2ns=2×109 seconds

Number of emitted photons =2.5×1015

Formulas to be used:

Energy =Nhω

Where N = number of emitted photons during the pulse source

h= Planck’s constant =6.626×1034

ω=frequencyoftheradiationsource

Frequency of source=1Durationofthesource

Calculation:

Step 1: Find frequency of source

1Durationofthesource

12×109=0.5×109

Step 2: Substituting

N=2.5×1015

h=6.626×1034

ω=0.5×109

In the energy formula, we get ,

Energy =(2.5×1015)(6.626×1034)(0.5×109)=8.28×1010 J

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