Consider an electron in the $\mathrm{n}=3$ orbit of a hydrogen-like atom with atomic number Z . At absolute temperature T , a neutron having thermal energy kaT 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, $\mathrm{k}_{\mathrm{B}}$ is the Boltzmann constant, $\mathrm{m}_{\infty}$ is the mass of the neutron and $\mathrm{a}_0$ is the first Bohr radius of hydrogen atom) then the value of $\alpha$ is $\_\_\_\_$