If the de Broglie wavelengths associated with a proton and an \(\alpha\)-particle are equal, then the ratio of velocities of the proton and the \(\alpha\)-particle will be :
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- 4 : 1
- 2 : 1
- 1 : 2
- 1 : 4
The Correct Option is A
Solution and Explanation
Given \(\lambda_p = \lambda_\alpha\), so \(m_p v_p = m_\alpha v_\alpha\).
\(\dfrac{v_p}{v_\alpha} = \dfrac{m_\alpha}{m_p}\).
An \(\alpha\)-particle has mass number 4 and a proton has mass number 1, so \(m_\alpha \approx 4 m_p\).
\(\dfrac{v_p}{v_\alpha} = \dfrac{4}{1}\), i.e. 4 : 1.
Answer: (1) 4 : 1
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