Question

De-Broglie wavelength of particle moving at a (1/4) th of speed of light having rest mass mo is…….. 

(A) {(3.87h) / (moC)} 

(B) {(4.92h) / (moC)} 

(C) {(7.57h) / (moC)} 

(D) {(9.46h) / (moC)}

Answer 1

The correct option is (A) {(3.87h) / (m_oC)}.

Explanation:

λ = (h/p) and p = mV hence λ = (h / mV) .....(1)

also m = [m_o / √{1 – (V² / C²)}]

given V = (C / 4) hence m = m_o = [m_o / √{1 – (C² / 16) × (1 / C²)}]

∴ m = [m_o / {√(15 / 16)}] = {(4m_o) / (√15)}

∴ from (1),

 λ = [h / ({4m_o / √15}V)]

= [h / ({4m_o / √15} × {C/4})]

= {(h√15) / (m_oC)}

= {(3.87h) / (m_oC)}