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BITSAT 2023Paper 1

Exam: BITSAT
Year: 2023
Paper: Paper 1
Subject: Physics
Chapter: Dual Nature of Matter

BITSAT 2023 · Paper 1 · Physics · Dual Nature of Matter

Proton (p) and electron (e) will have same deBroglie wavelength...

Proton (p) and electron (e) will have same deBroglie wavelength when the ratio of their momentum is (assume,

m_p=1849 \mathrm{ m}_{\mathrm{e}}

)

Options

A $1: 43$
B $43: 1$
C $1: 1849$
D $1: 1$

Correct answer

D. $1: 1$

Step-by-step solution

De Broglie wavelength is

\lambda=\frac{\mathrm{h}}{\mathrm{mv}}

\lambda_{\mathrm{p}}=\lambda_{\mathrm{e}} \Rightarrow \frac{\mathrm{h}}{\mathrm{m}_{\mathrm{p}} \mathrm{v}_{\mathrm{p}}}=\frac{\mathrm{h}}{\mathrm{m}_{\mathrm{e}} \mathrm{v}_{\mathrm{e}}}

\mathrm{m}_{\mathrm{e}} \mathrm{v}_{\mathrm{e}}=\mathrm{m}_{\mathrm{p}} \mathrm{v}_{\mathrm{p}} \Rightarrow \mathrm{p}_{\mathrm{e}}=\mathrm{p}_{\mathrm{p}}

\therefore \frac{\mathrm{p}_{\mathrm{p}}}{\mathrm{p}_{\mathrm{e}}}=\frac{1}{1}

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