The de Broglie wavelengths of a proton and an α particle are λ and 2λ respectively.

Question

The de Broglie wavelengths of a proton and an \(\alpha\) particle are \(\lambda\) and \(2\lambda\) respectively. The ratio of the velocities of proton and \(\alpha\) particle will be : 

(1) 1 : 8 

(2) 1 : 2 

(3) 4 : 1 

(4) 8 : 1

Answer 1

Correct option is (4) 8 : 1

\(P=\frac{h}{\lambda}\)

\(mv=\frac {h}{\lambda}\) ⇒ \(v=\frac {h}{m\lambda}\)

\(\frac{v_p}{v_{\alpha}}=\frac {m_{\alpha }\lambda _{\alpha}}{m_p \lambda _p}= \frac {4m_p \times 2\lambda}{m_p \times \lambda}=8:1\)