Q.341. de Broglie wavelength.

Question 341.
Calculate the de Broglie wavelength for a proton with a kinetic energy of 100 eV.

Answer 341.
E = (1/2) mv^2 = (mv)^2 / (2m = p^2/2m
=> p = √(2mE)

de Broglie wavelength,
λ = h/p


Mass of proton = 1.67262158 × 10-27 kilograms
Planck's constant, h = 6.626068 × 10-34 m2 kg / s
K.E. given = 100 eV = 100 x 1.60217646 × 10-19 joule

=> de Broglie wavelength, λ
= (6.626068 × 10-34) / [√(2 * 1.67262158 x 10^-27) * (100 x 1.60217646 x 10^-19)) m
= 2.862 x 10-12 m.

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