Question

a) Show that in F-D statistics, if level j is fully occupied with one particle per state w and there is only one way of distributing the particles among the energy state of that level (b) Calculate the value of nj in which an oxygen atom confined to a cubical box lcm on a side will have the same energy as the lowest energy available to a helium atom con fined to acubical bor 2x 10m on a side. 10

PLEASE KINDLY ATTEMPT ALL QUESTIONS. THANK YOU.

Answer 1

Answer :-

(a) Fermions obey pauli's exclusive principle which states that no two fermions can occupy the same quantum, state.

So, in each state only one fermion can occupy.

Quantum state corresponds to value of n, l, m.

Average number f particle (or) fermions in Jth state are

<nj>

(b) Energy of a particle in a cubical box is given by.

For helium atom, lowest energy is available for nx = ny = nz = 1.

nj = 3, also mass of helium.

m = 4 x 1.675 x 10^-2 Kg

Volume V = (2 x 10^-10)³

= 8 x 10^-30m³

For oxygen, V = (0.01)³

= 10^-6m³

according to question,