Dual Nature of Matter

JEE Main level, single correct, medium

78 of 200

Question 78 of 200

If the de Broglie wavelengths associated with a proton and an α\alpha-particle are equal, then the ratio of velocities of the proton and the α\alpha-particle will be:

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Answer: (C) 4:14: 1

According to question, λp=λα\lambda_p=\lambda_\alpha
Using, λ=hp=hmv\lambda=\frac{h}{p}=\frac{h}{m v}
 So, hmp×vp=hmα×vα⇒vpvα=mαmp=4mpmp\begin{aligned} &\text { So, } \frac{h}{m_p \times v_p}=\frac{h}{m_\alpha \times v_\alpha} \\ &\Rightarrow \frac{v_p}{v_\alpha}=\frac{m_\alpha}{m_p}=\frac{4 m_p}{m_p} \end{aligned}

(∵(\because mass of α\alpha-particle is 4 times of mass of proton)
So, vpvα=41\frac{v_p}{v_\alpha}=\frac{4}{1}; i.e., 4:14: 1

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