Correct Answer - Option 1 :
\(\frac{h}{{\sqrt {2mE} }}\)
Concept:
de Broglie wavelength of electrons:
- Louis de Broglie theorized that not only light possesses both wave and particle properties, but rather particles with mass - such as electrons - do as well,i.e. matter has dual nature.
- The wavelength of material waves is also known as the de Broglie wavelength.
- de Broglie wavelength (λ) of electrons can be calculated from Plancks constant h divided by the momentum of the particle
- So, according to de Broglie, every object has a dual nature- a particle and a wave nature whose wavelength is given by
\(\lambda = \frac{h}{{mv}}\) --
or \(\lambda = {h\over p}\) -- (1)
The relationship between momentum and Kinetic Energy is given as
\(p = \sqrt{2mE}\) -- (2)
Calcualtion:
If we put Equation (1) in Equation (2) we get
\(\lambda = {h\over \sqrt{2mE}}\)
So, the correct option is \(\frac{h}{{\sqrt {2mE} }}\)