Question

What is the frequency of a photon that has the same momentum as a neutron moving with a speed of 1.90 × 103 m/s?

Answer 1

The mass of a neutron is:

`m=1.67 \cdot 10^(-27)kg`
Since we know its speed, we can calculate the neutron's momentum:

`p=mv=(1.67 \cdot 10^(-27)kg)(1.90 \cdot 10^3 m/s)=3.17 \cdot 10^(-24) kg m/s`

The problem says the photon has the same momentum of the neutron, p. The photon momentum is given by

`p= (h)/(\lambda)`
where h is the Planck constant, and
`\lambda` 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:

`\lambda= (h)/(p)= (6.6 \cdot 10^(-34)Js)/(3.17 \cdot 10^(-24) kg m/s)=2.08 \cdot 10^(-10) m`

And since we know the photon travels at speed of light c, we can now calculate the photon frequency:

`f= (c)/(\lambda)= (3 \cdot 10^8 m/s)/(2.08 \cdot 10^(-10) m)= 1.44 \cdot 10^(18) Hz`