Dual Nature of Matter and Radiation

The de-Broglie wavelength is given by: λ=‌

h

√2mk

Step 2: Rearranging to Find Kinetic Energy
We can rearrange the formula to find kinetic energy k:λ2=‌

h2

2mk

So, k=‌

h2

2mλ2

Step 3: Substitute the Values
Here,
Planck's constant, h=6.6×10−34Js
Mass of electron, m=9×10−31kg
Wavelength, λ=2nm=2×10−9m
Now substitute these into the formula: k=‌

(6.6×10−34)2

2×9×10−31×(2×10−9)2

Step 4: Calculation
Calculate the value: k=‌

(6.6×10−34)2

2×9×10−31×(2×10−9)2

This gives: k=0.608×10−19J
Step 5: Convert Joules to Electron Volts
1 electron volt (eV)=1.6×10−19J.
So, k=‌

0.608×10−19

1.6×10−19

eV=0.38eV
The kinetic energy of the electron is about 0.38 eV .