deBroglie Relations and the scale of Quantum Effects, light waves as particles (b)

ii. a microwave operates at roughly $2.5 GHz$ at a max power

of $7.5 *10^9 erg/s$

How many photons per second can it emit? What about a 

low-power laser ($10^4 erg/s$ at $532nm$)?

Ans:

1.First for the microwave, 

The energy of one such microwave photon is $E = h v$

where the frequency v is $2.5*10^9 Hz$

so:

$E = 6.63*10^{-27}*2.5*10^9$

$E = 1.657*10^{-17}erg$

This is the energy, we have the power in erg/s which is $7.5*10^9erg/s$, to find the number of photons emitted we need to divide the power by the energy:

$\text{number of photons }=\frac{P}{E}$

$\text{number of photons }=\frac{7.5*10^9}{1.657*10^{-17}}$

$\text{number of photons }= 4.5265*10^{26}$

2.Now for the Laser,

Since now except the frequency, we have the wavelength we can substitute the formula of frequency in our energy formula:

$E=h*(\frac{c}{\lambda})$

where the frequency v is $2.5*10^9 Hz$ 

so:

$E = 6.63*10^{-27}*2.5*10^9$

$E = 1.657*10^{-17}erg$

$E=6.63*10^{-27}*(\frac{299,792,458}{532*\frac{1}{1*10^{9}}})$

$E=3.73*10^{-12}erg$

Now divide it with power:

$\frac{1*10^4}{3.73*10^{-12}} = 2.7*10^{15}photons$