A cylindrical rod of some laser material `5xx10^-2`m long and `10^-2m` in diameter contains `2xx10^25` ions per `m^3`. If on excitation all the ions are in the upper energy level and de-excite simultaneously emitting photons in the same direction , calculate the maximum energy contained in a polse of radiation of wavlength `6.6xx10^-7`m. If the pulse lasts for `10^-7s`, calculate the average power of the laser during the pulse.

Explanation

Total no. of ions in the rod=no. of ions per unit volumexvolume of rod
`=(2xx10^(25))xxpir^(2)l`
=`(2xx10^(25))xx[3.14xx(0.005)^(2)xx(5xx10^(-2))]`
`7.85xx10^(19)`
The number of photons emitted in one direction is equal to the total number of ions de excited. Therefore, the maximum energy contained in a pulse.
= no. of emitted photonsxenergy of photon
`=(7.85xx10^(19))xx(hc//lambda)`
`=(7.85xx10^(19))xx((6.6xx10^(-34))xx(3xx10^(8)))/(6.6xx10^(-7))`
`23.55xx10^(7)W=235.5MW`