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Q.

The ratio between acceleration of the electron in singly ionised helium atom and doubly ionised lithium atom (both in ground state) is

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a

$\frac{9}{4}$

b

$\frac{27}{8}$

c

$\frac{4}{9}$

d

$\frac{8}{27}$

answer is C.

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Detailed Solution

$a = \frac{v^{2}}{r} or a \propto \frac{(Z^{2})}{(1 / Z)}$

$∴ a \propto Z^{3}$

For singly ionised helium atom, Z = 2
and doubly ionised lithium atom, Z = 3

$\Rightarrow \frac{a_{{He}^{+}}}{a_{{Li}^{+ +}}} = \frac{(2)^{3}}{(3)^{3}} = \frac{8}{27}$

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