GATE Chemistry Practice Quiz

Question 1

For a particle in a one-dimensional infinite potential box of length L, which statement about the allowed energy levels is correct?

Accepted Answer

The energy levels are proportional to n^2/L^2.

Question 2

The normalized wavefunction of a particle in a 1D box is psi_n(x)=sqrt(2/L) sin(n pi x/L). For n=2, how many nodes are present inside the box (excluding the boundaries)?

Accepted Answer

1

Question 3

A particle in a 1D infinite box is in the state psi(x)=sqrt(2/L) sin(3 pi x/L). What is the expectation value of position <x>?

Accepted Answer

L/2

Question 4

For the hydrogen atom, how many radial nodes are present in the 3p orbital?

Accepted Answer

1

Question 5

A particle is confined in a 1D infinite box from x=0 to x=L. In the ground state, at which position is the probability density maximum?

Accepted Answer

x = L/2

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