Match the following ratio of De-Broglie wavelengths of a proton and ( α ) particle, when both ( List-I List-II A Have same speed (p) 2 : 1 B Have same potential difference (q) 1 : 1 C Have same kinetic energy (r) 4 : 1

Correct answer: B. ( array |c|c|c|c|c| & A & B & C & D 2 & r & s & p & q array ( aligned & (A) λ=(h)/(m v) or λ (1)/(m) & λ_ p λ_α = m_α m_ p =(4)/(1)( m_α 4 m_ p ) & (B) λ= h 2 mqV or λ 1 m · q & λ_ p λ_α = ( m_α m_ p )( q_α q_ p ) = (4)/(1) × (2)/(1) = 2 2 1 & ( . q_α=2 q_ p ) aligned ) (C) ( aligned & λ= h 2 mE_ k or λ 1 m & λ_ p λ_α = m_α m_ p = (4)/(1) =(2)/(1) aligned ) (D) ( aligned & λ= h p & λ_ p λ_α =(1)/(1) aligned )

NEET

Exam: NEET
Subject: Physics
Chapter: Dual Nature of Matter

NEET · Physics · Dual Nature of Matter

Match the following ratio of De-Broglie wavelengths of a proton and...

Match the following ratio of De-Broglie wavelengths of a proton and (

\alpha

) particle, when both (

	List-I		List-II
A	Have same speed	(p)	2 : 1
B	Have same potential
	difference	(q)	1 : 1
C	Have same kinetic
	energy	(r)	4 : 1
D	Have same linear
	momentum	(s)	2 $\sqrt{2}$ : 1

)

Options

A( $\begin{array}{|c|c|c|c|c|} \hline & A & B & C & D \\ \hline 1 & p & q & r & s \\ \hline \end{array}$
B( $\begin{array}{|c|c|c|c|c|} \hline & A & B & C & D \\ \hline 2 & r & s & p & q \\ \hline \end{array}$
C( $\begin{array}{|c|c|c|c|c|} \hline & A & B & C & D \\ \hline 3 & p & r & q & s \\ \hline \end{array}$
D( $\begin{array}{|c|c|c|c|c|} \hline & A & B & C & D \\ \hline 4 & r & q & s & p \\ \hline \end{array}$

Correct answer

B. ( $\begin{array}{|c|c|c|c|c|} \hline & A & B & C & D \\ \hline 2 & r & s & p & q \\ \hline \end{array}$

Step-by-step solution

(

\begin{aligned} & \text{ (A) } \lambda=\frac{h}{m v} \text{ or } \lambda \propto \frac{1}{m} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=\frac{\mathrm{m}_\alpha}{\mathrm{m}_{\mathrm{p}}}=\frac{4}{1}\left(\therefore \mathrm{ m}_\alpha \approx 4 \mathrm{ m}_{\mathrm{p}}\right) \\ & \text{ (B) } \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}} \text{ or } \lambda \propto \frac{1}{\sqrt{\mathrm{ m} \cdot \mathrm{q}}} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=\sqrt{\left(\frac{\mathrm{m}_\alpha}{\mathrm{m}_{\mathrm{p}}}\right)\left(\frac{\mathrm{q}_\alpha}{\mathrm{q}_{\mathrm{p}}}\right)}=\sqrt{\frac{4}{1} \times \frac{2}{1}}=\frac{2 \sqrt{2}}{1} \\ & \text{ (} \left.\therefore \mathrm{q}_\alpha=2 \mathrm{q}_{\mathrm{p}}\right) \end{aligned}

) (C) (

\begin{aligned} & \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}_{\mathrm{k}}}} \text{ or } \lambda \propto \frac{1}{\sqrt{\mathrm{ m}}} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=\sqrt{\frac{\mathrm{m}_\alpha}{\mathrm{m}_{\mathrm{p}}}}=\sqrt{\frac{4}{1}}=\frac{2}{1} \end{aligned}

) (D) (

\begin{aligned} & \lambda=\frac{\mathrm{h}}{\mathrm{p}} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=\frac{1}{1} \end{aligned}

)

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