The magnitude of acceleration of the electron | vedclass

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(A) The acceleration of an electron in the $n$th orbit is given by $a_{n} = \frac{v_{n}^{2}}{r_{n}}$.From Bohr's model,the velocity $v_{n} \propto \fr

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$1: 8$

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(A) The acceleration of an electron in the $n$th orbit is given by $a_{n} = \frac{v_{n}^{2}}{r_{n}}$.From Bohr's model,the velocity $v_{n} \propto \frac{Z}{n}$ and the radius $r_{n} \propto \frac{n^{2}}{Z}$.Substituting these into the acceleration formula:$a_{n} \propto \frac{(Z/n)^{2}}{(n^{2}/Z)} = \frac{Z^{2}/n^{2}}{n^{2}/Z} = \frac{Z^{3}}{n^{4}}$.Thus,the ratio of acceleration for hydrogen $(Z_{H} = 1)$ and singly ionised helium $(Z_{He} = 2)$ in the same $n$th orbit is:$\frac{a_{H}}{a_{He}} = \frac{Z_{H}^{3}}{Z_{He}^{3}} = \left(\frac{1}{2}\right)^{3} = \frac{1}{8}$.Therefore,the ratio is $1:8$.

The magnitude of acceleration of the electron in the $n$th orbit of a hydrogen atom is $a_{H}$ and that of a singly ionised helium atom is $a_{He}$. The ratio of $a_{H} : a_{He}$ is

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