The electron in a hydrogen atom makes a transition n1 → n2 where n1 and n2 are the principal quantum number of the two states. Assume the Bohr model to be valid. The time period of electron in the initial state is eight times that of the final state. The possible values of n1 and n2 are

Engineering

Physics

Spectrum of Hydrogen and Hydrogen Like Atoms

Bohrs Model of Atom

Question

The electron in a hydrogen atom makes a transition n₁ → n₂ where n₁ and n₂ are the principal quantum number of the two states. Assume the Bohr model to be valid. The time period of electron in the initial state is eight times that of the final state. The possible values of n₁ and n₂ are

n₁ = 8, n₂ = 1

n₁ = 8, n₂ = 2

n₁ = 6, n₂ = 3

n₁ = 4, n₂ = 2

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$T = \frac{2 πr}{v}$

mvr = n(h/2π)

$T = (\frac{4 π^{2} m}{nh}) r^{2}$

$r = n^{2} (\frac{h^{2} ε_{0}}{{πme}^{2}})$

$T = n^{3} (\frac{4 h^{3} ε_{0}^{2}}{{me}^{4}})$

$\frac{T_{1}}{T_{2}} = {(\frac{n_{1}}{n_{2}})}^{3}$