De-Broglie hypothesized that material particles have wave like properties. Figure shows a small particle in a box. The particle simply bounces back and forth at constant speed. As particles also have wave like properties it can be considered to be a wave reflecting back and forth from the ends of the box. The reflections will create a standing wave analogous to standing wave on a string tied at both ends. Since a standing wave confined to a region can have only selected wavelength, momentum of the particle is quantized. We can safely assume that such a particle only has kinetic energy. This energy must also be quantized.

What is the particle's energy in n^(th) state?

Options

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

Answer

A

Explanation

`1/lambda=RZ^(2)(1/n^(2)-1/m^(2))`
for H visible is form `2rightarrow3,4,5,6`……….
here`z=2`
`Rightarrow 1/lambda=R(Z^(2)/n^(2)-Z^(2)/m^(2))=R(4/4^(2)-4/m^(2))4/m^(2)=1/6^(2)`
`m=6 to 4,7 to 4`,…….