De Broglie Hypothesis

The de Broglie wavelength (

%5Clambda

) of a particle is given by the equation:

%5Clambda%20%3D%20%5Cfrac%7Bh%7D%7Bmv%7D

Where: -

h%20%3D%206.626%20%5Ctimes%2010%5E%7B-34%7D%20%5C%2C%20%5Ctext%7BJ.s%7D

(Planck's constant) -

m%20%3D%209.1%20%5Ctimes%2010%5E%7B-31%7D%20%5C%2C%20%5Ctext%7Bkg%7D

(mass of the electron) -

v%20%3D%200.2c

(velocity of the electron, 20% of speed of light) Given

c%20%3D%203%20%5Ctimes%2010%5E8%20%5C%2C%20%5Ctext%7Bm%2Fs%7D

, we have:

v%20%3D%200.2%20%5Ctimes%203%20%5Ctimes%2010%5E8%20%3D%206%20%5Ctimes%2010%5E7%20%5C%2C%20%5Ctext%7Bm%2Fs%7D

Substituting the values:

%5Clambda%20%3D%20%5Cfrac%7B6.626%20%5Ctimes%2010%5E%7B-34%7D%7D%7B(9.1%20%5Ctimes%2010%5E%7B-31%7D)(6%20%5Ctimes%2010%5E7)%7D%20%3D%201.2%20%5Ctimes%2010%5E%7B-11%7D%20%5C%2C%20%5Ctext%7Bm%7D

Thus, the de Broglie wavelength is

1.2%20%5Ctimes%2010%5E%7B-11%7D%20%5C%2C%20%5Ctext%7Bm%7D

Chapter Questions
1 MCQs