What is the moment of inertia of the electron | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

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

Vedclass · Answer

(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)

Similar Questions

Let $r, v, E$ be the radius of orbit,speed of electron,and total energy of electron respectively in a $H$-atom. Which of the following quantities,according to Bohr theory,is proportional to the quantum number $n$?

The ratio of the total energy of the $2^{\text{nd}}$ orbit electron for the hydrogen atom $(_1H^1)$ to that of the helium ion $(He^+)$ $(_2^4He)$ is:

The total energy of an electron $E_n = -\frac{Z^2me^4}{8\epsilon_0^2n^2h^2}$ in an atom is based on which hypothesis? Under what condition is this formula true?

Consider an electron in the $n^{th}$ orbit of a hydrogen atom in the Bohr model. The circumference of the orbit can be expressed in terms of the de Broglie wavelength $\lambda$ of that electron as

Vedclass Test Series

Exam Paper Generator

Online Exam Module