The basic idea of Quantum Mechanics is that motion in any system is quantized. The system obeys Classical Mechanics except that not every motion is allowed, only those motions which obey the `Bohr`-Sommerfeid Quantization.
`ointvecP.dvecr=nh,n in N`.
where `vecP` is the momentum, `vecr` is the position , `vecr` is the position vector and the integral is carried over a closed path. Assuming this is applicable to a particle of mass `m` moving with a constant speed in a box of lenth `L` having eleastic collisions with the walls of the box. Answer the following questions. `(h=6.6xx10^(-34)J-"sec."L=3.3A,m=10^(-30)kg)`

The allowed kinetic energy of the particle is :

Options

A. `(n^(2)h^(2))/(8pi^(2)mL^(2))`
B. `(n^(2)h^(2))/(2mL^(2))`
C. `(n^(2)h^(2))/(8mL^(2))`
D. `(n^(2)h^(2))/(32mL^(2))`

Explanation

Kinetic energy `E=(P^(2))/(2m)`
`E=(n^(2)h^(2))/(8mL^(2))`