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

Answer 1

To determine: The energy of pulsed radiation source  

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

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

$\omega$ = frequency of the radiation source

Frequency of source = $\frac { 1 }{ Duration\quad of\quad the\quad source }$

Calculation:

Step 1: Find frequency of source

$\frac { 1 }{ Duration\quad of\quad the\quad source }$

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

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

Answer 2

HEY MATE.....

HERE IS YOUR ANSWER....☺✌☺

$\huge\red{8.28×10^-10}$

I HOPE IT IS HELPFUL...☺✌☺