The electric potential between a proton and a | vedclass

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

Question

(A) The potential energy $U$ is given by $U = eV = eV_0 \ln(r/r_0)$.The force $F$ is given by $F = -dU/dr = -d/dr(eV_0 \ln(r/r_0)) = -eV_0/r$. The mag

Vedclass · Accepted Answer

$r_n \propto n$

Vedclass · Answer

(A) The potential energy $U$ is given by $U = eV = eV_0 \ln(r/r_0)$.The force $F$ is given by $F = -dU/dr = -d/dr(eV_0 \ln(r/r_0)) = -eV_0/r$. The magnitude of the force is $F = eV_0/r$.This force provides the necessary centripetal force for circular motion: $mv^2/r = eV_0/r$.Simplifying this,we get $mv^2 = eV_0$,which implies $v = \sqrt{eV_0/m}$. Note that $v$ is independent of $r$ and $n$.According to Bohr's quantization condition,the angular momentum is $mvr = nh/(2\pi)$.Substituting $v = \sqrt{eV_0/m}$ into the quantization condition,we get $m(\sqrt{eV_0/m})r_n = nh/(2\pi)$.Solving for $r_n$,we get $r_n = (nh / (2\pi)) \cdot \sqrt{1/(meV_0)}$.Since $h, m, e, V_0$ are constants,we conclude that $r_n \propto n$.

The electric potential between a proton and an electron is given by $V = V_0 \ln(r/r_0)$,where $r_0$ is a constant. Assuming Bohr's model to be applicable,find the variation of $r_n$ with $n$,where $n$ is the principal quantum number.

Similar Questions

The radius of the first (lowest) orbit of the hydrogen atom is $a_0$. The radius of the second (next higher) orbit will be (in $a_0$)

For an electron moving in the $n^{th}$ orbit of an $H$-atom,the angular velocity is proportional to:

In a hydrogen atom and a $Li^{2+}$ ion,the electron is in the second excited state. If $l_{H}$ and $l_{Li}$ are the angular momenta of the electrons and $E_H$ and $E_{Li}$ are their respective energies,then:

Consider an electron revolving in a circular orbit of a hydrogen atom,whose quantum number is $n=2$. The velocity of the electron in that orbit is

An electron is revolving in $n = 3$ orbit. What will be the magnetic field at the centre of the hydrogen atom? (in $T$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module