The mass of a neutron is:
[tex]m=1.67 \cdot 10^{-27}kg[/tex]
Since we know its speed, we can calculate the neutron's momentum:
[tex]p=mv=(1.67 \cdot 10^{-27}kg)(1.90 \cdot 10^3 m/s)=3.17 \cdot 10^{-24} kg m/s[/tex]
The problem says the photon has the same momentum of the neutron, p. The photon momentum is given by
[tex]p= \frac{h}{\lambda} [/tex]
where h is the Planck constant, and [tex]\lambda[/tex] 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:
[tex]\lambda= \frac{h}{p}= \frac{6.6 \cdot 10^{-34}Js}{3.17 \cdot 10^{-24} kg m/s}=2.08 \cdot 10^{-10} m [/tex]
And since we know the photon travels at speed of light c, we can now calculate the photon frequency:
[tex]f= \frac{c}{\lambda}= \frac{3 \cdot 10^8 m/s}{2.08 \cdot 10^{-10} m}= 1.44 \cdot 10^{18} Hz[/tex]
