Q. 354.5( 4 Votes )

# Find the typical

Answer :

Given:

Pressure, P = 1 atm = 101325 Pa

Temperature, T = 27° = 300K

De-Broglie wavelength is given by,  …(1)

Where,

h = Planck’s constant = 6.6 × 10-34 Js

m = mass of He

E = total energy

Mass of helium, m = Atomic mass/ number of atoms

Let there be one mole of He,

mass of 1 mol of He = 4 g

Then,

m = 4/ 6.023 × 1023

m = 6.64 × 10-24 = 6.64 × 10-27Kg …(2)

We know that average energy at temperature T is given by,

E = 3/2 kT …(3)

Where,

k = Boltzmann constant = 1.38 × 10-23 Jmol-1K-1

T = absolute temperature

Using the equation (3), we can rewrite equation (1) as, …(4)

Putting the values in equation (4) we get, λ = 0.72 × 10-10m

Using ideal gas equation we have,

PV = RT

PV = kNT Where,

V = volume

N = number of moles

P = pressure

k = Boltzmann constant

T = absolute temperature

Mean distance between, r is given by,  r = 3.3 × 10-9m

The mean separation between the atoms is greater than the De- Broglie wavelength.

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