If the radius of the first orbit of hydrogen | vedclass

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(B) The radius of the $n^{th}$ orbit of a hydrogen atom is given by $r_n = a_0 n^2$. For the $3^{rd}$ orbit $(n = 3)$, the radius is $r_3 = a_0 	imes

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$6$

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(B) The radius of the $n^{th}$ orbit of a hydrogen atom is given by $r_n = a_0 n^2$. For the $3^{rd}$ orbit $(n = 3)$, the radius is $r_3 = a_0 	imes 3^2 = 9 a_0$. According to Bohr's postulate, the circumference of the orbit is an integral multiple of the de Broglie wavelength: $2 \pi r_n = n \lambda$. Substituting the values for the $3^{rd}$ orbit: $2 \pi (9 a_0) = 3 \lambda$. Solving for $\lambda$: $\lambda = \frac{18 \pi a_0}{3} = 6 \pi a_0$.

If the radius of the first orbit of hydrogen atom is $a_0$, then de Broglie's wavelength of electron in $3^{rd}$ orbit is (in $\pi a_0$)

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