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JIPMER 2017

Exam: JIPMER
Year: 2017
Subject: Physics
Chapter: Atomic Physics

JIPMER 2017 · Physics · Atomic Physics

The potential of an atom is given by V=V_0 _e (r / r_0) where r_0...

The potential of an atom is given by

V=V_0 \log _e

\left(r / r_0\right)

where

r_0

is a constant and

r is the radius of the orbit. Assuming Bohr's model to be applicable, which variation of

r_n

with

n

is possible (

n

being principal quantum number)?

Options

A $r_n \propto n$
B $r_n \propto 1 / n$
C $r_n \propto n^2$
D $r_n \propto 1 / n^2$

Correct answer

A. $r_n \propto n$

Step-by-step solution

Given that,

V=V_0 \log _e\left(r / r_0\right)

Field

E=-\frac{d V}{d r}=-V_0\left(\frac{r}{r_0}\right)

\begin{aligned} & e E=\frac{m V^2}{r} \text{ or } \frac{e V_0 I_0}{r}=\frac{m V^2}{r} \\ & V=\left(\frac{e V_0 I_0}{m}\right)^{1 / 2}\end{aligned}

m V=\left(m_e V_0 r_0\right)^{1 / 2}=

constant

\therefore m v r=\frac{n h}{2 \pi}

, Bohr's quantum condition or $r \propto n

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