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(B) The acceleration $a$ of an electron in a circular orbit is given by $a = \frac{v^2}{r}$.From Bohr's theory,the velocity $v \propto \frac{Z}{n}$ an

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$8$

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(B) The acceleration $a$ of an electron in a circular orbit is given by $a = \frac{v^2}{r}$.From Bohr's theory,the velocity $v \propto \frac{Z}{n}$ and the radius $r \propto \frac{n^2}{Z}$.Substituting these into the acceleration formula: $a \propto \frac{(Z/n)^2}{n^2/Z} = \frac{Z^2/n^2}{n^2/Z} = \frac{Z^3}{n^4}$.Since both atoms are in the ground state,$n = 1$ for both.Therefore,$a \propto Z^3$.The ratio of acceleration for singly ionized helium $(Z=2)$ to hydrogen $(Z=1)$ is $\frac{a_{He^+}}{a_H} = \left( \frac{Z_{He^+}}{Z_H} \right)^3 = \left( \frac{2}{1} \right)^3 = 8$.

The ratio between the total acceleration of the electron in a singly ionized helium atom and a hydrogen atom (both in the ground state) is:

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