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 number of ions in the rod
=number of ions per unit volume`xx` volume of rod
`=(2xx10^(25))xx3.14xx(0.005)^(2)xx(5xx10^(-2))`
`=7.85xx10^(19)`
The number of photons excited in one direction is equal to the total number of ions because all ions are excited Noe, excited energy
=number of excited photons`xx` energy of photon
`(7.85xx10^(19))xx(hc)/(lamda)`
`=(7.85xx10^(19))xx((6.6xx10^(-34))xx(3xx10^(8)))/(6.6xx10^(-7))`
`=23.55W`