SATHEE: Atoms And Nuclei Question 282

Atoms And Nuclei Question 282

Question: Suppose an electron is attracted towards the k origin by a force $\frac{k}{r}$ where A: 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 nth orbital of the electron is found to be $‘ r_{n}^{'}$ and the kinetic energy of the electron to be $‘ K_{n}^{'}$ . Then winch of the following is true

Options:

A) $K_{n}$ independent of n, $r_{n} \propto n$

B) $K_{n} \propto \frac{1}{n}, r_{n} \propto n$

C) $K_{n} \propto \frac{1}{n}, r_{n} \propto n^{2}$

D) $K_{n} \propto \frac{1}{n^{2}}, r_{n} \propto n^{2}$

Show Answer

Answer:

Correct Answer: A

Solution:

$\frac{m v^{2}}{r} = \frac{K}{r} or v = \sqrt{\frac{K}{m}} = c r^{\circ}$ Now $m v r = \frac{n h}{2 π} or r = \frac{n h}{2 π m v}$
$∴ r \propto n .$ Also kinetic energy $K = \frac{m v^{2}}{2} = \frac{m}{2} \times \frac{K}{m} = \frac{K}{2} .$

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Atoms And Nuclei Question 282

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