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}{a \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 [JEE Adv 2025 P1]

Dual Nature of Radiation

Section: Physics

Question : 2 of 24

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

z2h2

aπ2a02mNkB

, (where h is the Planck's constant, kB is the Boltzmann constant, mN is the mass of the neutron and a0 is the first Bohr radius of hydrogen atom) then the value of α is ‌‌‌‌

[JEE Adv 2025 P1]

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