JEE Main · PhysicsHard

$A particle of mass m is confined in a one-dimensional box of length L . The ratio of the energy difference between the third and second excited states to the energy difference between the second and first excited states is:$

Show correct answer & step-by-step solution

Correct answer: B — $7/5$

Solution

The energy levels are E_{n} = n^{2} E_{1} . The first excited state is n = 2, second is n = 3, and third is n = 4 . The differences are E_{4} - E_{3} = (16 - 9) E_{1} = 7 E_{1} and E_{3} - E_{2} = (9 - 4) E_{1} = 5 E_{1} . The ratio is 7/5 .