Ratio of centripetal acceleration for an electron revolving in $3^{\text {rd }}$ and $5^{\text {th }}$ Bohr…

Ratio of centripetal acceleration for an electron revolving in $3^{\text {rd }}$ and $5^{\text {th }}$ Bohr orbit of hydrogen atom is
  1. $425: 18$
  2. $625: 81$
  3. $125: 27$
  4. $221: 36$

Solution

Centripetal acceleration $\mathrm{a}=\frac{\mathrm{v}^2}{\mathrm{r}}$ For hydrogen atoms, $\mathrm{v} \propto \frac{1}{\mathrm{n}}$ and $\mathrm{r} \propto \mathrm{n}^2$ $\begin{aligned} & \therefore \mathrm{a} \propto \frac{1}{\mathrm{n}^4} \\ & \therefore \frac{\mathrm{a}_3}{\mathrm{a}_5}=\left(\frac{5}{3}\right)^4=\frac{625}{81} \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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