What is the moment of inertia of the electron | vedclass

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(C) The moment of inertia $I$ of an electron of mass $m$ moving in an orbit of radius $r$ is given by $I = mr^2$.The radius of the $n^{	ext{th}}$ Boh

Vedclass · Accepted Answer

$\frac{16 \varepsilon_0^2 h^4}{\pi^2 m e^4}$

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(C) The moment of inertia $I$ of an electron of mass $m$ moving in an orbit of radius $r$ is given by $I = mr^2$.The radius of the $n^{	ext{th}}$ Bohr orbit is given by the formula:$r_n = \frac{\varepsilon_0 h^2 n^2}{\pi m e^2}$For the second Bohr orbit,$n = 2$. Substituting $n = 2$ into the formula:$r_2 = \frac{\varepsilon_0 h^2 (2)^2}{\pi m e^2} = \frac{4 \varepsilon_0 h^2}{\pi m e^2}$Now,calculate the moment of inertia $I$ for the second orbit:$I = m 	imes (r_2)^2$$I = m 	imes \left( \frac{4 \varepsilon_0 h^2}{\pi m e^2} ight)^2$$I = m 	imes \frac{16 \varepsilon_0^2 h^4}{\pi^2 m^2 e^4}$$I = \frac{16 \varepsilon_0^2 h^4}{\pi^2 m e^4}$

What is the moment of inertia of the electron moving in the second Bohr orbit of a hydrogen atom? ($h=$ Planck's constant,$m=$ mass of electron,$\varepsilon_0=$ permittivity of free space,$e=$ charge on electron)

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