JEE Main · PhysicsHard
A particle of mass $m$ is confined in a one-dimensional box of length $L$. The energy difference between the first excited state and the ground state is $\Delta E$. If the length of the box is doubled, the new energy difference is what fraction of $\Delta E$?
- A.1/2
- B.1/4
- C.1/8
- D.1
Show correct answer & step-by-step solution
Correct answer: B — 1/4
Solution
The energy levels are given by . The energy difference is proportional to , so doubling reduces the energy difference by a factor of 4.
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