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JEE Advanced levelSingle correct optionDifficulty 3 of 3as147

Treat an electron as a standing wave in a one-dimensional box of length $L$ ( $λ = 2 L / n$ ) with $E = p^{2} /2 m$ . If the box length is doubled, the energy of the $n = 2$ level of the new box compared with the $n = 1$ level of the original box is

Aone-fourth
Bequal
Chalf
Dfour times larger

Answer: B

E_{n} = n^{2} h^{2} / (8 m L^{2})

. New

E_{2} = 4 h^{2} / (8 m \cdot 4 L^{2}) = h^{2} / (8 m L^{2})

, which equals the original

E_{1}

.

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