Question

A nonrelativistic electron has a larger de Broglie wavelength than a nonrelativistic proton. Which one of the following statements about these particles must be accurate? A) The proton has more momentum than the electron

B) Both particles have the same kinetic energy.

C) The proton has more kinetic energy than the electron.

D) The electron has more kinetic energy than the proton.

E) The electron has more momentum than the proton.

Answer is A. Pleas explain step by step how you got this answer.

Answer 1

de Broglie equation: λ = h/p = h/mv = h/(2mE)1/2 = v/f
where p is momentum and E is the kinetic energy
λ is inversely proportional to p
λ of electron is larger than proton
therefore momentum (p) of proton is larger than electron p.
Now λ is inversely proportional to square root of E and m, also E is proportional to p but inversely to m
E = p^2/2m
As m of electron is smaller than proton but p of electron is smaller than proton, hence it cannot be said accurately if the E of electron is greater, smaller or equal to those of proton's.
Therefore the answer is A.