Question

The ratio of total acceleration of the electrons in singly ionized helium atom and hydrogen atom (both in ground state) is -

Assume uniform circular motion of electrons.

• A. $1:1$
• B. $8:1$
• C. $4:1$
• D. $6:1$

Answer 1

The correct option is B $8:1$

For uniform circular motion of electrons,

Acceleration, $a\propto \frac{v^2}{r}$

Also,

$v\propto \frac{Z}{n}$

$r\propto \frac{n^2}{Z}$

$\therefore a\propto \frac{Z^3}{n^4}$

Since both atoms are in ground state $i.e.n=1$

$\Rightarrow a\propto Z^3$

So,

$\frac{a_{H{e}^{+}}}{a_H}={\left(\frac{Z_{H{e}^{+}}}{Z_H}\right)}^3={\left(\frac{2}{1}\right)}^3=\frac{8}{1}=8:1$

Hence, option $\left(B\right)$ is the correct answer.