Complete GATE PH 2024 Paper 1 overview, original pages and practice · Timed previous-paper practice

Questions 13–15 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 5 of 22

Question 13

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The wavefunction of a particle in an infinite one-dimensional potential well at time

is

where

,

and

are the normalized ground state, the normalized first excited state and the normalized second excited state, respectively.

,

and

are the eigen-energies corresponding to

,

and

, respectively. The expectation value of energy of the particle in state

is
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Question 14

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If a thermodynamic system is adiabatically isolated and experiences a change in volume under an externally applied constant pressure, then the thermodynamic potential minimized at equilibrium is the
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Question 15

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The mean distance between the two atoms of HD molecule is

, where H and D denote hydrogen and deuterium, respectively. The mass of the hydrogen atom is

. The energy difference between two lowest lying rotational states of HD in multiples of

is
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