Question

h
3) Quantum mechanics is relevant, when the de Broglie wavelength of the particle is
greater than the distance between particles. The purpose of this problem is to determine
which systems will have to be treated quantum mechanically and which can be
described classically.
a) Show that the typical de Broglie wavelength of a particle in an ideal gas in
equilibrium is 2 =
3mK9T
b) Solids: The lattice spacing in a typical solid is d 0.3 nm. Find the temperature
below which the free electrons in a solid are quantum mechanical? (Hint: Refer the
a) part of the question and treat free electrons as a gas and the lattice spacing as the
typical distance between the electrons)
c) Gases: For what temperatures are the atoms in an ideal gas at pressure P quantum
mechanical? (Hint: Use the ideal gas law. to deduce the inter atomic distance)
Is Helium at atmospheric pressure quantum mechanical?
What about Hydrogen atoms in outer space (interatomic distance is 1 cm and
temperature is 3 K)?
(5 marks)​

Answer 1

Answer:

Explanat  Quantum mechanics is relevant, when the de Broglie wavelength of the particle is

greater than the distance between particles. The purpose of this problem is to determine

which systems will have to be treated quantum mechanically and which can be

described classically.

a) Show that the typical de Broglie wavelength of a particle in an ideal gas in

equilibrium is 2 =

3mK9T

b) Solids: The lattice spacing in a typical solid is d 0.3 nm. Find the temperature

below which the free electrons in a solid are quantum mechanical? (Hint: Refer the

a) part of the question and treat free electrons as a gas and the lattice spacing as the

typical distance between the electrons)

c) Gases: For what temperatures are the atoms in an ideal gas at pressure P quantum

mechanical? (Hint: Use the ideal gas law. to deduce the inter atomic distance)

Is Helium at atmospheric pressure quantum mechanical?

What about Hydrogen atoms in outer space (interatomic distance is 1 cm and

temperature is 3 K)?