Quantum Mechanics Answers

Estimate the Hydrogen Ground State Energy

Is it possible to see inside an atom?

A typical atomic nucleus is about 5 × 10−15 m in radius. Use the uncertainty principle to place a lower limit on the energy an electron must have if it is to be part of a nucleus. 

What is a quantum? 

 Compare QM and classical results.

Explain the atomic spectrum of the Hydrogen using Bohr Model.

Using the Plank’s theory, show that ρ(ν)dν = 8πν2 c 3 hν e hν kBT − 1 dν

 Using the classical theory, derive the formula ρ(ν)dν = 8πν2 c 3 kBT dν for the blackbody radiation where ρ(ν) is the energy per unit of volume in the frequency interval ν to ν + dν of the blackbody spectrum of a cavity at temperature T.

A container holds 2 moles of a diatomic gas at temperature T = 420K. At this temperature,

rotational motions (but not vibrational motions) of the gas molecules are allowed.

(a) What is the total internal energy of this gas? (2)

(b) A quantity of energy E = 300 Joules is transferred to the gas. What fraction of this added

energy is responsible for increasing the temperature of the gas? (1)

(c) How much did the internal translational energy increase, and thus how much did the temperature

of the gas increase? (4)

(d) Explain how the predictions from particle statistics fail, when describing the heat capacities

of a diatomic ideal gas.

Show that low-frequency limit of Planck’s Law reduces to the Rayleigh-Jeans Law

and in the high-frequency limit reduces to Wien’s Law