question_answer

The de-Broglie wavelength of a particle of kinetic energy K is \[\lambda \]. What would be the wavelength of the particle, if its kinetic energy were\[K/4\] ?                  

Answer:

              de Broglie wavelength of a particle of mass m and kinetic energy K is \[\lambda =\frac{h}{\sqrt{2mK}}\] When the kinetic energy is \[K/\text{4}\], \[\lambda '=\frac{h}{\sqrt{2mK/4}}=\frac{2h}{\sqrt{2mK}}=2\lambda .\]