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JEE Main 2008

Exam: JEE Main
Year: 2008
Subject: Physics
Chapter: Atomic Physics

JEE Main 2008 · Physics · Atomic Physics

Suppose an electron is attracted towards the origin by a force k /...

Suppose an electron is attracted towards the origin by a force

k / r

where '

k

' is a constant and '

r

' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the

n^{\text{th }}

orbital of the electron is found to be '

r_n

' and the kinetic energy of the electron to be

T_n

. Then which of the following is true?

Options

A $T_n \propto 1 / n^2, \quad r_n \propto n^2$
B $T_n$ independent of $n, r_n \propto n$
C $T_n \propto 1 / n, \quad r_n \propto n$
D $T_n \propto 1 / n, \quad r_n \propto n^2$

Correct answer

B. $T_n$ independent of $n, r_n \propto n$

Step-by-step solution

\begin{aligned}& \frac{\mathrm{k}}{\mathrm{r}}=\frac{m v^2}{\mathrm{r}}\\ & \mathrm{mv}=\mathrm{k} \quad \text{ (independent or }r \text{ ) }\\ & \mathrm{n}\left(\frac{\mathrm{h}}{2 \pi}\right)=m v r \Rightarrow r \propto \mathrm{n} \text{\text{ and } } \mathrm{T}=\frac{1}{2}m v² \text{ is independent\text{ of } } \mathrm{n} . \end{aligned}

$$

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