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Sagot :
The frequency of a photon is 1.06 * [tex]10^{18}[/tex] Hz.
The mass of a neutron is:
m = 1.67 * [tex]10^{-27}[/tex] kg
Since we know its speed, we can calculate the neutron's momentum:
p = mv = (1.67 * [tex]10^{-27}[/tex] kg)(1400 m/s) = 2.34 * [tex]10^{-24}[/tex] kg m /s
The problem says the photon has the same momentum of the neutron, p. The photon momentum is given by
p = h / λ
where h is the Planck constant, and λ is the photon wavelength. If we re-arrange the equation and we use the momentum we found before, we can calculate the photon's wavelength:
p = h / λ = [6.6 * [tex]10^{-34}[/tex] J/s] / [2.34 * [tex]10^{-24}[/tex] kg m /s ]
= 2.82 * [tex]10^{-10}[/tex] m
And since we know the photon travels at speed of light c, we can now calculate the photon frequency:
f = c / λ = [3 * [tex]10^{8}[/tex] m/s] / [ 2.82 * [tex]10^{-10}[/tex] m ]
= 1.06 * [tex]10^{18}[/tex] Hz.
Learn more about photon frequency here :
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