Answer:
Wavelength = 64.635 pm
Explanation:
The expression for the deBroglie wavelength and kinetic energy is:
[tex]\lambda=\frac {h}{\sqrt{2\times m\times K.E.}}[/tex]
Where,
[tex]\lambda[/tex] is the deBroglie wavelength
h is Plank's constant having value [tex]6.626\times 10^{-34}\ Js[/tex]
m is the mass of electron having value [tex]9.11\times 10^{-31}\ kg[/tex]
K.E. is the kinetic energy of the electron.
Given, K.E. = 360 eV
Energy in eV can be converted to energy in J as:
1 eV = 1.6022 × 10⁻¹⁹ J
So, K.E. = [tex]360\times 1.6022\times 10^{-19}\ J=5.76792\times 10^{-17}\ J[/tex]
Applying in the equation as:
[tex]\lambda=\frac {h}{\sqrt{2\times m\times K.E.}}[/tex]
[tex]\lambda=\frac{6.626\times 10^{-34}}{\sqrt {{2\times 9.11\times 10^{-31}\times 5.76792\times 10^{-17}}}}\ m[/tex]
[tex]\lambda=\frac{10^{-34}\times \:6.626}{\sqrt{10^{-48}\times \:105.0915024}}\ m[/tex]
[tex]\lambda=6.4635\times 10^{-11}\ m[/tex]
Also, 1 m = 10¹² pm
So, Wavelength = 64.635 pm
