JEE Main 2026 Apr 6 Shift 2, Physics Q22: Wave Nature of Matter

JEE Main2026Apr 6, Shift 2Physics

The de Broglie wavelength for an electron accelerated through the potential difference $V_{1}$ volt is $λ_{1}$ . When the potential difference is changed to $V_{2}$ volt, the associated de Broglie wavelength is increased by 50%. If $(V_{1} / V_{2}) = (9/ α)$ , then the value of $α$ is _____.

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Solution

For an electron accelerated through $V$ : $λ = \frac{h}{2 m e V}$ , so $λ \propto \frac{1}{V}$ .

$\frac{λ _{2}}{λ _{1}} = \frac{3}{2} = \frac{V _{1}}{V _{2}}$ $\Rightarrow$ $\frac{V _{1}}{V _{2}} = \frac{9}{4}$ .

$∴ α = 4$ .

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JEE Main 2026 Apr 6 Shift 2, Physics Q22: Wave Nature of Matter

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