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

To solve the problem step by step, we will first calculate the total number of ions in the cylindrical rod, then determine the maximum energy contained in a pulse of radiation, and finally calculate the average power of the laser during the pulse.

### Step 1: Calculate the Volume of the Cylindrical Rod
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height (length) of the cylinder.
...