The ground state energy of an electron in an infinite well is 1 eV. What will be the ground state energy if the width of the well is doubled?

Q.1 (f) The ground state energy of an electron in an infinite well is 1 eV. What will be the ground state energy if the width of the well is doubled?

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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Formula: \(E_n=\dfrac{n^2h^2}{8mL^2}\), so for the ground state \(E_1\propto\dfrac{1}{L^2}\).

\[ \frac{E_1'}{E_1}=\Big(\frac{L}{L'}\Big)^2=\Big(\frac{L}{2L}\Big)^2=\frac14 \]

\(E_1'=\dfrac{1}{4}\times1\ \text{eV}\)

New ground-state energy = 0.25 eV

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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The ground state energy of an electron in an infinite well is 1 eV. What will be the ground state energy if the width of the well is doubled?

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