Hydrogen atom is bombarded with electrons accelerated through a potential different of V, which causes excitation of hydrogen atoms. If the experiment is being formed at T = 0 K. The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be V = α/10, where α = ________.
Physics · Atomic Structure and X-rays · Atomic Structure & Bohr's Atomic Model
JEE Mains 2024 29 Jan Evening Shift

Question

Hydrogen atom is bombarded with electrons accelerated through a potential different of V, which causes excitation of hydrogen atoms. If the experiment is being formed at T = 0 K. The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be V = α/10, where α = ________.

Physics · Atomic Structure and X-rays · Atomic Structure & Bohr's Atomic Model

JEE Mains 2024 29 Jan Evening Shift

G1 Physics · Accepted Answer

For minimum potential difference electron has to make transition from n = 3 to n = 2 state but first electron has to reach to n = 3 state from ground state. So, energy of bombarding electron should be equal to energy difference of n = 3 and n = 1 state. ΔE = 13.6[1 – 1/3²] = eV V = (13.6 × 8)/9 V = 12.09 V ≈ 12.1 V So, α = 121