Ratio of centripetal acceleration for an elec | vedclass

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(B) The centripetal acceleration is given by $a = \frac{v^2}{r}$.For a hydrogen atom,the velocity of an electron in the $n^{	ext{th}}$ orbit is $v \p

Vedclass · Accepted Answer

$625: 81$

Vedclass · Answer

(B) The centripetal acceleration is given by $a = \frac{v^2}{r}$.For a hydrogen atom,the velocity of an electron in the $n^{	ext{th}}$ orbit is $v \propto \frac{1}{n}$ and the radius is $r \propto n^2$.Substituting these into the expression for acceleration:$a \propto \frac{(1/n)^2}{n^2} = \frac{1}{n^4}$.Therefore,the ratio of centripetal acceleration for the $3^{	ext{rd}}$ and $5^{	ext{th}}$ orbits is:$\frac{a_3}{a_5} = \left(\frac{5}{3}ight)^4 = \frac{625}{81}$.

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

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