Question

How do you calculate the speed of a 3.1eV photon and a 3.1eV electron?

Answer 1

Step-by-step explanation:

We need to find the speed of a 3.1eV proton and a 3.1eV electron.

For proton, using conservation of energy such that,

`(1)/(2)m_pv_p^2=eV\\\\v_p^2=(2eV)/(m_p)\\\\v_p=\sqrt{(2eV)/(m_p)}`

`m_p` is mass of proton

`v_p=\sqrt{(2* 3.1* 1.6* 10^(-19)\ J)/(1.67* 10^(-27)\ kg)}\\\\v_p=2.43* 10^5\ m/s`

For electron,

`(1)/(2)m_ev_e^2=eV\\\\v_e^2=(2eV)/(m_e)\\\\v_e=\sqrt{(2eV)/(m_e)}`

`m_e` is mass of proton

`v_e=\sqrt{(2* 3.1* 1.6* 10^(-19)\ J)/(9.1* 10^(-31)\ kg)}\\\\v_e=1.44* 10^6\ m/s`

Hence, this is the required solution.