quantum mechanics part 1

what is the wavelength?

the distance between two wave crests or troughs

what is the frequency?

the number of wave crests that pass over the origin every second

what is black body radiation?

the light radiated by an object when it’s hot

what is emitted when light is shone on a metal surface?

what is expected to happen (energy)? what actually happens?

how was this resolved?

electrons

energy of electrons should depend on intensity of incident light. instead, electrons are emitted above a certain frequency of UV

resolved by considering light as photons

what is the equation for kinetic energy of ejected electron?

m is mass

v is speed

Φ is work function of material (energy to remove electron from surface)

how does the atomic spectrum of hydrogen hint at quantisation?

when heat or electrical energy is applied, it emits an atomic spectrum with discrete wavelengths

• only certain frequencies are emitted

• different for each element

emission spectrum

• appearance

• where are transitions to and from?

• what does spectral line look like?

bright lines against dark background

transitions are from higher to lower energy levels

absorption spectrum

• appearance

• where are transitions to and from?

• what does spectral line look like?

dark line against bright background

transitions are from low to high energy levels

what are Paschen series transitions?

Transitions to n=3

what are Balmer series transitions?

transitions to n=2

what are Lyman series transitions?

transitions to n=1

what is the equation for frequency of light in Hz for hydrogen?

R_H is the Rydberg constant (=3.29×10¹⁵ Hz )

n₁, n₂ are integers representing ELs

what is the difference between constructive and destructive interference of waves?

constructive = in phase

destructive = out of phase

how does amplitude change with constructive and destructive interference?

constructive = waves add to give greater amplitude

destructive = cancel out to give reduced/zero amplitude

what was Bohr’s model of the atom?

electrons move around the nucleus in a fixed orbit

why do macroscopic objects not show perceptible wave like properties?

the de Broglie wavelength is too small

how to calculate angular momentum?

L=mvr

r is radius of orbit

how to calculate centripetal force?

how to calculate electrostatic force?

Q₁ and Q₂ are point charges

ε₀ is constant, permittivity of free space

what does quantisation mean?

there are discrete levels of energies in an atom, rather than continuous spectrum

what were the problems with Bohr’s model?

·      He couldn’t explain the quantisation condition for angular momentum.

·      Classically, an orbiting charged particle would emit electromagnetic radiation, lose energy and fall into the nucleus.

·      While the model could explain the atomic spectrum of hydrogen, it couldn’t predict the spectra of other atoms.

what is the time independent Schrödinger equation?

what is kinetic energy

what is potential energy

kinetic = energy of motion

potential = dependent on position

what is the wavefunction ψ (psi) - what does it contain info about

is it directly measurable?

contains info on the properties and behaviour of a particle but is not directly measurable

what is ψ² proportional to?

the probability of finding the particle in a small volume dV

what is ψ² for electrons?

electron density

what is the Heisenberg uncertainty principle?

what does l describe

orbital angular quantum number

how many nodes - ie which orbital it isw

what does m_l describe

magnetic quantum number

the direction of the orbital

how to calculate x,y,z using polar coordinates?

x=r sin⁡θ cos⁡ϕ

y=r sin⁡θ sin⁡ϕ

z=r cos⁡θ

what is the radial wavefunction dependent on?

n and l

what does the angular wavefunction depend on?

l and m_l

how many nodes does

s orbital

p orbital

d orbital

f orbital have?

s is n-1

p is n-2

d is n-3

f is n-4

why is the s orbital spherically symmetric?

no angular dependence

which orbitals are not zero at the nucleus (radial nodes)?

s orbitals

what are the radial nodes graph shapes for n =1,2,3?

where is the highest probability for the electron in radial distribution functions?

the maximum value is most probable distance

what is the spin quantum number?

which way is clockwise/anticlockwise?

represents the direction of spin, m_s = ± ½

what is the Aufbau principle?

Lowest energy levels are filled first

what do the energy levels for multi-electron atoms depend on?

• principle quantum number n (which EL)

• orbital angular quantum number l (which orbital)

for hydrogen, what do energy levels depend on?

what does this explain?

energy levels depend only on n

• energy levels are degenerate for different values of l and m_l for given value of n

this is why Bohr model worked for hydrogen

what is Pauli exclusion principle?

no two electrons in same region of space can have the same 4 quantum numbers (n, l, ml, ms)

• this means 2 electrons per orbital (ms = ± 1/2)

what happens to electrons when electron orbitals overlap?

electrons in different atoms with same quantum numbers repel

what are the different types of energy stored?

electronic, vibration, rotation, translation

why can the different forms of energy stored in a molecule be treated independently?

electronic transitions are much faster than bond vibrational motion, faster than rotations, faster than translational motion

in particle in a box, what is the potential energy inside the box?

0

in particle in a box, what is the potential energy outside the box?

∞

what is the wavefunction at the edge of the box?

how does this affect quantisation?

0

the particle cannot exist in regions of space where 𝜓 (𝑥) = 0, so confinement leads to quantisation of energy levels

what is the energy inside the box?

all energy is kinetic

how does increasing particle size affect wavelength and ΔE?

increases emission wavelength and decreases gaps between ELs