Respuesta :
Explanation:
It is known that formula for momentum per photon is as follows.
p = [tex]\frac{h}{\lambda}[/tex]
where, [tex]\lambda[/tex] is the photon's wavelength.
Putting the given values into the above formula as follows.
p = [tex]6.626 \times 10^{-34} Joule seconds}{600 \times 10^{-9}}m[/tex]
= [tex]1.10 \times 10^{-27} kg ms^{-1}[/tex]
Therefore, the value of linear momentum is [tex]1.10 \times 10^{-27} kg ms^{-1}[/tex] .
Now, energy per photon is calculated as follows.
E = [tex]\frac{hc}{\lambda}[/tex]
where, h = Planck's constant ([tex]6.626 \times 10^{-34}[/tex] Joule seconds),
c = the velocity of light ([tex]3 \times 10^{8}[/tex] m/s).
Hence, calculate the energy as follows.
E = [tex]\frac{hc}{\lambda}[/tex]
= [tex]6.626 \times 10^{-34} Joule seconds \times 3 \times 10^{8} m/s}{600 \times 10^{-9} m[/tex]
= [tex]3.3 \times 10^{-19}[/tex] J
Hence, the value of energy per photon is [tex]3.3 \times 10^{-19}[/tex] J.
Now, we will calculate the energy per mole of photons as follows.
E = [tex]\frac{Nhc}{\lambda}[/tex]
where, E = the energy in a mole of photons,
N = Avogadro's number ([tex]6.02 \times 10^{23}[/tex] photons per mole),
h = Planck's constant ([tex]6.626 \times 10^{-34}[/tex] Joule seconds),
c = the velocity of light ([tex]3 \times 10^{8}[/tex] m/s)
Putting these given values into the above formula and calculate the energy per mole of photons as follows.
E = [tex]\frac{Nhc}{\lambda}[/tex]
= [tex]\frac{6.02 \times 10^{23} \times 6.626 \times 10^{-34} \times 3 \times 10^{8}}{600 \times 10^{-9}}[/tex]
= 199 kJ/mol
Therefore, energy per mole of photons for radiation of wavelength for 600 nm (red) is 199 kJ/mol.
