Quantum Mechanics Answers

find Approximation transmission probability in quantum mechanics E<U

With a neat diagram, explain the working of electron microscopes. Briefly explain the 

 role of each experimental component. Compare the resolution of electron microscopes 

 and optical microscopes.

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 𝜆 = ℎ/√3𝑚𝐾𝐵𝑇

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)?

 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)

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 𝜆 = ℎ/√3𝑚𝐾𝐵𝑇

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)?

caluculate the Resolution of electron microscopes and optical microscopes

Equation of Quantum hormonic oscillator in terms of. m and omega.

find the Expectation value of. [xp]-[px] indetail

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  𝜆 =

ℎ/√3𝑚𝐾𝐵𝑇

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)

Below what temperature, is Helium at atmospheric pressure quantum mechanical?

Below what temperature is Hydrogen atoms in outer space quantum mechanical? 

(interatomic distance is 1 cm and temperature is 3 K)

find Approximation transmission probability in quantum mechanics E<U