The accleration of the electron in first Bohr orbit in hydrogen atom is :
(where $A_{0}$ = Bohr's radius, m = mass of electron and $h$ = $\frac{h}{2 π}$ )

\frac{h^{2}}{m^{2} a_{0}^{3}}

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\frac{h^{2} m^{2}}{a_{0}^{3}}

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\frac{h^{2} - a_{0}^{3}}{m^{2}}

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none of the above

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Solution

The correct option is B $\frac{h^{2}}{m^{2} a_{0}^{3}}$
For $n = 1, r = a_{o}$
Bohr's Angular momentum quantisation
$m v a_{o} = h$
$v = \frac{h}{m a_{o}}$ ----------(1)
Centirpetal Accelaration $= \frac{v^{2}}{r} = \frac{v^{2}}{a_{o}} = \frac{h^{2}}{m^{2} a_{o}^{3}}$

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Ψ = \frac{1}{\sqrt{π}} {(\frac{1}{a_{0}})}^{3 / 2} e^{- π / a_{0}}

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