Practicing Success

Target Exam

CUET

Subject

Chemistry

Chapter

Structure of Atom

Question:

According to Bohr's theory of H-atom, for the electron in the nth permissible orbit :

Options:

\(\text{Linear momentum} \propto \frac{1}{n}\)

\(\text{Angular Momentum} \propto n\)

\(\text{Kinetic Energy } \propto \frac{1}{n^2}\)

All of the above

Correct Answer:

All of the above

Explanation:

The correct answer is option 4. All of the above.

\(\text{Angular Momentum Quantization }\)

\(\text{mvr = }\frac{nh}{2\pi}\text{----------→(1)}\)

\(\text{Centripetal force:}\)

\(\frac{k(e)e}{r^2}\text{ = }\frac{mv^2}{r}\text{----------→(2)}\)

\(v^2r\text{ = }\frac{ke^2}{m}\)

\(\text{Substituting equation (1) in (2), we get}\)

\(\text{v = }\frac{2\pi ke^2}{nh}\)

\(\text{Energy: E = 13.6}\frac{Z^2}{n^2}\text{----------→(3)}\)

\(\text{Linear Momentum :}\)

\(\text{mvr = }\frac{nh}{2\pi r}\text{----------→(4)}\)

\(\text{From the concept attached :}\)

\(\text{r } \propto n^2\text{----------→(5)}\)

\(\text{Hence, mv  } \propto \frac{1}{n}\)

\(\text{and,  U = 2K.E. }\)

 \(E \propto \frac{1}{n^2}\)