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

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(A) According to Bohr's postulate, the circumference of the $n^{th}$ orbit is an integer multiple of the de Broglie wavelength:$2\pi r_n = n\lambda$Fo

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(A) According to Bohr's postulate, the circumference of the $n^{th}$ orbit is an integer multiple of the de Broglie wavelength:$2\pi r_n = n\lambda$For a hydrogen atom $(Z=1)$, the radius of the $n^{th}$ orbit is given by $r_n = a_0 n^2$.Substituting this into the Bohr quantization condition:$2\pi (a_0 n^2) = n\lambda$$2\pi a_0 n = \lambda$For the third orbit $(n=3)$:$\lambda = 2\pi a_0 (3)$$\lambda = 6\pi a_0$

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

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