Question

The momentum of a proton having energy equal to the rest energy of an electron is ??

Answer 1

The rest energy of an electron is found from `E = m.c^2` you then need to equate this to the K.E. of the proton and finally convert to momentum using `E_k = p^2/(2m)`

Explanation:

The rest energy of the electron is found from assuming all its mass is converted to energy. The masses in the two calculations are the mass of the electron and the proton respectively.

`E = m_e.c^2`
`E = 9.11 xx 10^-31.(3xx10^8)^2`
`E = 8.2 xx 10^-14 J`

`E = E_k`

`p = sqrt(2m_p.E_k)`
`p = sqrt(2xx1.627xx10^-27xx8.2xx10^-14)`
`p = 1.633xx10^-20 kg.ms^-1`

OK?