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

Ratio of centripetal acceleration for an electron revolving in $3^{\text {rd }}$ orbit to $5^{\text {th }}$ Bohr orbit of hydrogen atom is
  1. $\frac{424}{21}$
  2. $\frac{625}{81}$
  3. $\frac{125}{4}$
  4. $\frac{775}{61}$

Solution

Centripetal acceleration $\mathrm{a}=\frac{\mathrm{v}^{2}}{\mathrm{r}}$ $v \propto \frac{1}{n}$ and $r \alpha n^{2}$ $\therefore a=\frac{1}{n^{4}}$ $\therefore \frac{a_{5}}{a_{3}}=\frac{(3)^{4}}{(5)^{4}}=\frac{81}{125}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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