Wavelength And Frequency

Step 1: Using the de-Broglie wavelength formula.
The de-Broglie wavelength

%5Clambda

is given by:

%5Clambda%20%3D%20%5Cfrac%7Bh%7D%7B%5Csqrt%7B2%20m%20e%20V%7D%7D

where

h

is Planck’s constant (

6.626%20%5Ctimes%2010%5E%7B-34%7D%20%5C%2C%20%5Ctext%7BJs%7D

m

is the mass of the electron (

9.11%20%5Ctimes%2010%5E%7B-31%7D%20%5C%2C%20%5Ctext%7Bkg%7D

e

is the charge of the electron (

1.6%20%5Ctimes%2010%5E%7B-19%7D%20%5C%2C%20%5Ctext%7BC%7D

), and

V

is the potential difference (100 volts).
Step 2: Substituting the known values.
Substitute the known values into the formula:

%5Clambda%20%3D%20%5Cfrac%7B6.626%20%5Ctimes%2010%5E%7B-34%7D%7D%7B%5Csqrt%7B2%20%5Ctimes%209.11%20%5Ctimes%2010%5E%7B-31%7D%20%5Ctimes%201.6%20%5Ctimes%2010%5E%7B-19%7D%20%5Ctimes%20100%7D%7D

After calculation, we find:

%5Clambda%20%5Capprox%201.226%20%5C%2C%20%5Ctext%7Bnm%7D

Step 3: Conclusion.
The de-Broglie wavelength of the electron is approximately

1.226%20%5C%2C%20%5Ctext%7Bnm%7D

Chapter Questions
1 MCQs