Consider an electron in the orbit of a hydrogen-like atom with atomic number

CHEMISTRY · Numerical · CBSE · Chemistry · Structure of Atom · Structure of Atom

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^2h^2}{\alpha\pi^2a_0^2m_nk_B}

, where

h

is Planck's constant,

k_B

is Boltzmann's constant,

m_n

is the mass of the neutron, and

a_0

is the first Bohr radius of the hydrogen atom, find

\alpha