A muon (mu^-) is a negatively charged particl | vedclass

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

Question

(D) The radius of an orbit is given by $r_n = \frac{\epsilon_0 n^2 h^2}{\pi m Z e^2}$. Since $r \propto \frac{1}{m}$,the radius of the muonic orbit $r

Vedclass · Accepted Answer

$(A), (C), (D)$

Vedclass · Answer

(D) The radius of an orbit is given by $r_n = \frac{\epsilon_0 n^2 h^2}{\pi m Z e^2}$. Since $r \propto \frac{1}{m}$,the radius of the muonic orbit $r_{\mu} = \frac{r_e}{200}$. Thus,$(A)$ is correct.The velocity of an electron in the $n^{th}$ orbit is $v_n = \frac{Z e^2}{2 \epsilon_0 n h}$. Since $v$ is independent of mass $m$,the speed of the muon is the same as that of the electron. Thus,$(B)$ is incorrect.The ionization energy is $E_n = \frac{m Z^2 e^4}{8 \epsilon_0^2 n^2 h^2}$. Since $E \propto m$,the ionization energy of the muonic atom $E_{\mu} = 200 E_H$. Thus,$(C)$ is correct.The momentum is $p = m v$. Since the velocity $v$ is the same for both and $m_{\mu} = 200 m_e$,the momentum of the muon is $200$ times that of the electron. Thus,$(D)$ is correct.Therefore,statements $(A), (C),$ and $(D)$ are correct.

Similar Questions

Consider a hydrogen atom with its electron in the $n^{\text{th}}$ orbital. An electromagnetic radiation of wavelength $90 \ nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4 \ eV$,then the value of $n$ is $(hc = 1242 \ eV \ nm)$.

An electron revolving in the $n^{\text{th}}$ Bohr orbit has a magnetic moment $\mu_n$. If $\mu_n \propto n^x$,the value of $x$ is:

When a hydrogen atom,initially at rest,emits a photon resulting in a transition $n = 5 \rightarrow n = 1$,its recoil speed is about

Instead of angular momentum quantisation,a student predicts that energy is quantised as $E = \frac{-E_{0}}{n}$,$(E_{0} > 0)$ and $n$ is a positive integer. Which of the following options is correct?

The magnetic moment of an electron due to its orbital motion is proportional to ($n$ = principal quantum number).

Vedclass Test Series

Exam Paper Generator

Online Exam Module