A mu-meson of charge 'e',mass 208 m_e moves i | vedclass

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

Question

(B) The radius of the $n$-th orbit in a hydrogen-like atom is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$.For the first Bohr orbit of a hy

Vedclass · Accepted Answer

$n \approx 25$

Vedclass · Answer

(B) The radius of the $n$-th orbit in a hydrogen-like atom is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$.For the first Bohr orbit of a hydrogen atom $(Z=1, m=m_e, n=1)$:$r_1 = \frac{h^2 \epsilon_0}{\pi m_e e^2}$.For the $\mu$-meson system $(Z=3, m=208 m_e)$:$r_n = \frac{n^2 h^2 \epsilon_0}{\pi (208 m_e) (3) e^2}$.Equating the two radii $(r_n = r_1)$:$\frac{n^2 h^2 \epsilon_0}{\pi (208 m_e) (3) e^2} = \frac{h^2 \epsilon_0}{\pi m_e e^2}$.Simplifying the equation:$\frac{n^2}{208 	imes 3} = 1$.$n^2 = 624$.$n = \sqrt{624} \approx 24.98 \approx 25$.

$A$ $\mu$-meson of charge '$e$',mass $208 m_e$ moves in a circular orbit around a heavy nucleus having charge $+3e$. The quantum state '$n$' for which the radius of the orbit is the same as that of the first Bohr orbit for a hydrogen atom is [approximately]:

Similar Questions

The ground state energy of a hydrogen atom is $-13.6 \text{ eV}$. What is the kinetic energy of the electron in this state (in $\text{ eV}$)?

An electron in a hydrogen atom makes a transition from $n_1$ to $n_2$. If the time period of the electron in the initial state is eight times that in the final state,then:

The velocity of an electron in the first Bohr orbit of $He^+$ ion is .......

An electron makes a transition from orbit $n = 4$ to the orbit $n = 2$ of a hydrogen atom. The wave number of the emitted radiations ($R =$ Rydberg's constant) will be

To accommodate the view that matter is made up of $5$ elements only,a scientist proposed the following hypothesis: atoms can have a maximum principal quantum number $n_{\max}$ and no higher. Then,which of the following statements must be true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module