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Wednesday, 25 June 2014

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






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