Question

A gamma spectrometer delivers a 10ns pulse of 1Mw average power. If the photons have a wavelength of 694.3nm, how many are contained in the pulse

Answer 1

To solve this task we need to calculate the energy of the one pulse first. This is done by using a formula:

$$E_{pulse}=P*t=1*10^6 W * 10*10^{-9} s = 10^{-2} J$$

where P - power, t - time of the pulse.

Now we need to calculate energy of the one photon at a given wavelength:

$$E= \frac {hc} {\lambda} = \frac { (6.626 × 10^{−34} J*s) (3*10^8 m/s) } {694.3 * 10^{-9} m} = 2.86 * 10^{-19} J$$

where h - Planck constant, c - light speed, lambda - wave length.

Now we can get number of photons by dividing total energy of the pulse by energy of the one photon:

$$E= \frac {E_{pulse}} {E_{photon}} = \frac { 10^{−2} J } {2.86 * 10^{-19} J} = 3.49 * 10^{16}$$

Answer: there are 3.49 * 10^16 photons in one pulse of the mentioned laser.