Answer:
a
[tex]n = 1.119 *10^{18} \ photons[/tex]
b
[tex]P = 1.6 \ W[/tex]
Explanation:
From the question we are told that
The wavelength is [tex]\lambda = 2780 nm = 2780 *10^{-9} \ m[/tex]
The energy is [tex]E = 80 mJ = 80 *10^{-3} \ J[/tex]
This energy is mathematically represented as
[tex]E = \frac{n * h * c }{\lambda }[/tex]
Where c is the speed of light with a value [tex]c = 3.0 *10^{8} \ m/s[/tex]
h is the Planck's constant with the value [tex]h = 6.626 *10^{-34} \ J \cdot s[/tex]
n is the number of pulses
So
[tex]n = \frac{E * \lambda }{h * c }[/tex]
substituting values
[tex]n = \frac{80 *10^{-3} * 2780 *10^{-9}}{6.626 *10^{-34} * 3.0 *10^{8} }[/tex]
[tex]n = 1.119 *10^{18} \ photons[/tex]
Given that the pulses where emitted 20 times in one second then the period of the pulse is
[tex]T = \frac{1}{20}[/tex]
[tex]T = 0.05 \ s[/tex]
Hence the average power of photons in one 80-mJ pulse during 1 s is mathematically represented as
[tex]P = \frac{E}{T}[/tex]
substituting values
[tex]P = \frac{ 80 *10^{-3}}{0.05}[/tex]
[tex]P = 1.6 \ W[/tex]
