The radius of the first orbit in an H-atom is | vedclass

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(B) The radius of the $n^{	ext{th}}$ orbit is given by $r_n = a_0 n^2$.For the third orbit $(n=3)$,the radius is $r_3 = a_0 	imes 3^2 = 9 a_0$.Accor

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$6$

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(B) The radius of the $n^{	ext{th}}$ orbit is given by $r_n = a_0 n^2$.For the third orbit $(n=3)$,the radius is $r_3 = a_0 	imes 3^2 = 9 a_0$.According to Bohr's quantization condition,the angular momentum is $mvr = \frac{nh}{2\pi}$.Rearranging for momentum $mv$,we get $mv = \frac{nh}{2\pi r}$.Substituting $n=3$ and $r=9a_0$:$mv = \frac{3h}{2\pi(9a_0)} = \frac{h}{6\pi a_0}$.The de-Broglie wavelength is $\lambda = \frac{h}{mv}$.Substituting the value of $mv$:$\lambda = \frac{h}{h / (6\pi a_0)} = 6\pi a_0$.

The radius of the first orbit in an $H$-atom is '$a_0$'. Then,the de-Broglie wavelength of the electron in the third orbit is: (in $\pi a_0$)

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