(B) The time period of revolution $T$ of an electron in a Bohr orbit is given by the formula $T \propto \frac{n^3}{Z^2}$.For the hydrogen atom $(H)$:

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(B) The time period of revolution $T$ of an electron in a Bohr orbit is given by the formula $T \propto \frac{n^3}{Z^2}$.For the hydrogen atom $(H)$: $n_1 = 2$,$Z_1 = 1$. Thus,$T_H \propto \frac{2^3}{1^2} = 8$.For the $He^{+}$ ion: $n_2 = 3$,$Z_2 = 2$. Thus,$T_{He^+} \propto \frac{3^3}{2^2} = \frac{27}{4}$.The ratio $\frac{T_H}{T_{He^+}} = \frac{8}{27/4} = \frac{8 \times 4}{27} = \frac{32}{27}$.

Class 11 Chemistry Structure of Atom Atomic models and Planck's quantum theory

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What is the ratio of the time period of revolution of an electron in the second orbit of a hydrogen atom to that in the third orbit of a $He^{+}$ ion?

A
$8 : 27$
B
$32 : 27$
C
$27 : 32$
D
None of these

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Structure of Atom

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Atomic models and Planck's quantum theory

The frequency of radiation absorbed or emitted when transition occurs between two stationary states with energies $E_1$ (lower) and $E_2$ (higher) is given by

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Which observations are not explained by the electromagnetic theory of physics?

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In the case of a hydrogen atom,when an electron falls from a higher energy level to the $M$ shell,the corresponding spectral line will form a part of:

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Rutherford's $\alpha$-particle scattering experiment concluded that:

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The frequency of one of the lines in the Paschen series of a hydrogen atom is $2.340 \times 10^{11} \ Hz$. The quantum number $n_2$ which produces this transition is

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What is the ratio of the time period of revolution of an electron in the second orbit of a hydrogen atom to that in the third orbit of a $He^{+}$ ion?

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