Question

The wavelength of an electron and a neutron will become equal when the velocity of the electron is x times the velocity of neutron. The value of x is ______. (Nearest integer)
(Mass of electron is 9.1 × 10-31 kg and mass of neutron is 1.6 × 10-27 kg)

Answer 1

$λ_e=\frac {h}{m_e×V_e}$

$λ_N=\frac {h}{m_N×V_N}$
Now,
$λ_e = λ_N$
When $V_e=xV_N$
$\frac {1}{m_eV_e}=\frac {1}{m_N×V_N}$

$\frac {m_N}{m_e}=\frac {V_e}{V_N}=x$

$x=\frac {1.6×10^{−27}}{9.1×10^{−31}}$

$x=0.17582×10^4$
$x≃1758$

So, the answer is $1758$.