If λe, λp and λα, be the de-Broglie wavelength of electron, proton and α-particle, respectively, then
Answer & explanation
Correct answer: option 4
Considering that the question indicates if the particles have same speed or K.E or accelerating potential. (Although not mentioned in question)
λ = \(\frac{h}{mv}\) or λ = \(\frac{h}{\sqrt{2m(KE)}}\) or λ = \(\frac{h}{\sqrt{2mqV}}\)
In all of the above possibilities
λ ∝ \(\frac{1}{\sqrt{mq}}\)
And mp = 1836 me , mα = 4mp
\( \sqrt{(m q)_e} < \sqrt{(m q)_p} < \sqrt{(m q)_\alpha} \)
∴ From the above relation
λα < λp < λe