If the radius of the first orbit of H atom is | vedclass

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(C) The radius of the $n^{th}$ orbit is given by $r_n = a_0 n^2$.For the third orbit $(n = 3)$, the radius is $r = a_0 	imes (3)^2 = 9 a_0$.According

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$6$

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

If the radius of the first orbit of $H$ atom is $a_0$, what is the de-Broglie wavelength of an electron in the third orbit (in $\pi a_0$)?

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