A 1 mW laser beam is incident onto a detector. Determine the fractional fluctuation in number of photons intercepted by the detector in a time interval T 1 us for photons with energy (a) E1 10 Me; (b) Ez 10 eV.

Respuesta :

Answer:

(a) [tex]625 photons[/tex]

(b)[tex]625\times 10^{6}photons[/tex]

Explanation:

Given that , the power of the laser beam is,

[tex]P=1 mW\\P=1\times 10^{-3} W[/tex]

and time is given is,

[tex]t=1\mu s\\t=10^{-6}s[/tex]

Now the energy formula for the laser beam is,

[tex]E=P\times t[/tex]

Now,

[tex]E=10^{-3}\times 10^{-6}  \\E=10^{-9}J[/tex]

(a) The value of energy is given,

[tex]E_{1}=10MeV\\E_{1}=10\times 10^{6}\times 1.6\times 10^{-19}J\\ E_{1}=16\times 10^{-13}J[/tex]

Now the no of photons's fraction fluctuation is,

[tex]n=\frac{E}{E_{1} }\\ n=\frac{10^{-9} }{16\times 10^{-13} }\\ E_{1}=625 photons[/tex]

Therefore the no of photons is [tex]625 photons[/tex].

(b)The value of energy is given,

[tex]E_{z}=10eV\\E_{z}=16\times 10^{-19}J[/tex]

Now the no of photons's fraction fluctuation is,

[tex]n=\frac{E}{E_{z} }\\ n=\frac{10^{-9} }{16\times 10^{-19} }\\n=625\times 10^{6}photons[/tex]

Therefore the no of photons is[tex]625\times 10^{6}photons[/tex].