Q. An electron is accelerated through a potential difference of V volt. It has a wavelength λ associated with it. Through what potential difference an electron must be accelerated so that its de-Broglie wavelength is the same as that of a proton? Take mass of proton to be 1837 times larger than the mass of electron.
(a) V volt
(b) 1837 V volt
(c) V/1837 volt
(d) √(1837)volt
Ans: (d)
Sol: λ = h/√(2meV)
λ’ = h/√(2m’eV’)
Since , λ = λ’
h/√(2meV) = h/√(2m’eV’)
m V =m’V’
m V = m×1837×V’
V’ = V/1837 volt