Question

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

Answer 1

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,

$\dfrac{1}{2}m_pv_p^2=eV\\\\v_p^2=\dfrac{2eV}{m_p}\\\\v_p=\sqrt{\dfrac{2eV}{m_p}}$

$m_p$ is mass of proton

$v_p=\sqrt{\dfrac{2\times 3.1\times 1.6\times 10^{-19}\ J}{1.67\times 10^{-27}\ kg}}\\\\v_p=2.43\times 10^5\ m/s$

For electron,

$\dfrac{1}{2}m_ev_e^2=eV\\\\v_e^2=\dfrac{2eV}{m_e}\\\\v_e=\sqrt{\dfrac{2eV}{m_e}}$

$m_e$ is mass of proton

$v_e=\sqrt{\dfrac{2\times 3.1\times 1.6\times 10^{-19}\ J}{9.1\times 10^{-31}\ kg}}\\\\v_e=1.44\times 10^6\ m/s$

Hence, this is the required solution.