For a particle of mass m enclosed in a one-dimentional box of length L, the de-Broglie concept would lead to stationary waves, with nodes at the two ends. The energy values allowed for such a system (with n as integers) will be:

Options

A. `(h^(2))/(8mL^(2))n^(2)`
B. `(h^(2))/(4mL)n^(2)`
C. `(h)/(4mL)n`
D. `(h^(2))/(4mL^(2))n^(2)`

Answer

A

Explanation

`lambda=(2L)/(n),p=(nh)/(2L) :. lambda=(p)/(h)`
`E=(p^(2))/(2m)=((nh)/(2L))^(2)*(1)/(2m)=(h^(2)n^(2))/(8mL^(2))`