Physics

Problem

Consider an electron in the

n = 3

orbit of a hydrogen-like atom with atomic number

Z

. At absolute temperature

T

, a neutron having thermal energy

k_B T

has the same de Broglie wavelength as that of this electron. If this temperature is given by

T = \frac{Z^2 h^2}{\alpha \pi^2 a_0^2 m_N k_B}

, (where

h

is the Planck's constant,

k_B

is the Boltzmann constant,

m_N

is the mass of the neutron and

a_0

is the first Bohr radius of hydrogen atom) then the value of

\alpha

is _____ .