A cylindrical rod of some laser material `5xx10^(-2)m` long and `10^(-2)m` diameter contains `2xx1025^(25)` ions per `m^(3)`. If on excitation all the ions in the upper energy level de-excite simultaneously emitting photons in the same direction, calculate the maximum energy contained in a pulse of radiation of wavelength `6.6xx10^(-7)m`

Options

A. `3xx10^(-17)J`
B. `3xx10^(-18)J`
C. `3xx10^(-19)J`
D. `3xx10^(-20)J`

Answer

C

Explanation

Volume of the rod `=pi r^(2)l`
`=3.14((1)/(2)xx10^(-2))^(2)xx5xx10^(-2)m^(3)`
`=3.925xx10^(-6)m^(3)`
Total number of ions, `N=2xx10^(25)xx3.925xx10^(-6)`
`=7.85xx10^(19)`
Energy of pulse `=(hc)/(lambda)=(6.6xx10^(-34)xx3xx10^(8))/(6.6xx10^(-7))`
`=3xx10^(-19)J`