Classical and Quantum Mechanics

Question 1

Newtons laws

Answer 1

1.Inertia: particles will move uniformly unless acted on by an exernal force 2. Particles will accelerate in propotion to mas applied and in inverse propotion to their mass 3. For every action there is an equal and opposite reaction

Question 2

Velocity, acceleration and force

Answer 2

Velocity: Atoms part of a gaseous state move with high velocity whereas those part of a solid vibrate in place Acceleration: Change of velocity per unit of time, depends on force and mass Force: Depends on the gradient of potential energy surface (-gradient)

Question 3

Energy and GIbbs free energy equation

Answer 3

Molecular systems move spontaneouly from high energy arrangements to low energy arrangements

Question 4

Potential and Kinetic energy

Answer 4

Energy of a system depends on kinetic energy which is associated with moving objects and potential energy which is stored in the system

Question 5

Limitations in classical mechanics

Answer 5

• Failure to predict wavelength of light distributed from a black body
• Failure to predict heat capacities of solids
• Failure to predict atomic and molecular spectra
• Observation that small particles such as electrons can act as waves

Question 6

Key aspects of quantim mechanics

Answer 6

• energy of small particles are quantitized: energy of particles can have discrete values energy changes can occur only in packages of a fixed size
• Wave/particle duality. Particles can have a fixed location in space or may behave like waves

Question 7

Properties of particles

Answer 7

• localized in space
• defined size
• can be reflected
• can be scattered

Question 8

Properties of waves

Answer 8

• not localized in space
• wavelength, amplitude, phase
• can be reflected
• can be diffracted
• form interference patterns

Question 9

Standing waves

Answer 9

when waves travelling in different directions interfere with eachother

i.e. when a guitar string is plucked

Question 10

Wave/particle experiment

Answer 10

youngs double slit experiment

Particles (i.e. electrons) are fired through a plate with a single slit and then pass through a plate with a double slit. An interfernce pattern results, even when electrons are fired one at a time

Question 11

Shrodinger equation

Answer 11

HΨ = EΨ

• provides descripitions of electron distribution in a molecule
• solves using computational methods

H= hamiltonian operator

E = energy operator

Trident= wave function

NEED TO CALCULATE THE WAVEFUNCTION OF ALL THE ELECTRONS IN THE SYSTEM, COMPUTATIONALLY DIFFUCULT AND SLOW

Question 12

Strengths and limitations of QM

Answer 12

Strengths: accurete, provides all electrons, models chemical interactions, calculates molecular orbitals and orbital energies

Limitations: Very slow, do not provide exact solutions to the shrodinger eqn, impractical on large molecules (proteins)