The mass of an electron is 9.1 × 10–31 kg. If its K.E. is 3.0 × 10–25 J, calculate its wavelength.

Given:

Mass of an Electron = 9.1 × 10–31 kg


Kinetic Energy, K.E. = 3.0 × 10–25 J


1/2 mv2 = kinetic Energy


Where


m = mass of electron


v = velocity of electron


v2 = [2× 3.0 × 10–25] / [9.1× 10-31]


= [6.0 × 10–25] / [9.1× 10-31]


v2 = 659.3406 × 103


Therefore v = √ [659.3406 × 103]


v = 811.99 m/s


According to the de Broglie’s Equation:


λ = h/mv


Where,


λ = wavelength of moving particle


m = mass of electron


v= velocity of particle


h= Planck’s constant [6.62× 10-34]


λ = {[6.62× 10-34] / [9.1× 10-31] × [811.99]}


= {[6.62× 10-34] / [7.389 × 10-28]


= 8.959× 10-7 m


Therefore, the wavelength is 8.96× 10-7 m


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