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{mv^{2}}{r}=\frac{K}{r}\text{ or }v=\sqrt{\frac{K}{m}}=cr{}^\circ $ Now $ mvr=\frac{nh}{2\pi }\text{ or }r=\frac{nh}{2\pi mv} $
$ \therefore r\propto n. $ Also kinetic energy $ K=\frac{mv^{2}}{2}=\frac{m}{2}\times \frac{K}{m}=\frac{K}{2}. $
