Question

An electron and a neutron have the same de Broglie wavelength. Which is true? (a) The electron has more kinetic energy and a higher speed. (b) The electron has less kinetic energy but a higher speed (c) The electron has less kinetic energy and a lower speed (d) The electron and neutron have the same kinetic energy but the electron has the higher speed (e) The neutron has more kinetic energy but the two have the same speed

Answer 1

Explanation:

The mass of electron, $m_e=9.1\times 10^{-31}\ kg$

The mass of neutron, $m_n=1.67\times 10^{-27}\ kg$

The De-Broglie wavelength is given by :

$\lambda=\dfrac{h}{p}$

p is the momentum, p = m v

For electron, $\lambda_e=\dfrac{h}{m_ev}$

For neutron, $\lambda_=\dfrac{h}{m_nv}$

Since, an electron and a neutron have the same de Broglie wavelength. So,

$\lambda_e=\lambda_n$

$m_ev_e=m_nv_n$

The mass of electron is less than the mass of neutron. So, the speed of electron is more than than the speed of neutron. As the kinetic energy is directly proportional to the mass. So, the correct option is (a) The electron has more kinetic energy and a higher speed.