week 2 Flashcards
what did de broglie propose?
all moving objects have a wavelength
all matter has wave-like properties
electrons are both waves and particles
give the wave-particle duality equation
λ=h/mv
λ is wavelength
h is planks constant
m is mass
v is velocity
how is the wave-particle duality equation derived?
know that E=h𝝂
know that 𝝂λ=c
sub in v into E=h𝝂=hc/λ
combine with E=mc^2
λ=h/mc –> λ=h/mv
(v velocity)
only works for when h is tiny so good for electrons
what is the phase of a wave
sign of the amplitude
can be positive, negative or zero
what does an area of zero amplitude mean
0 amplitude = node
eg where sinx wave intersects x-axis
as frequency increases…
- wavelength…
- energy…
- number of nodes…
- wavelength gets shorter
- energy increases
- number of nodes increases
what effects do electrons experience and what does this lead to? what does this suggest?
electrons experience interference and diffraction effects which lead to areas of higher and lower intensities = suggests electrons behave as waves
give the equation for quantisation of angular momentum
mvr = nh/2𝛑 m is mass v is velocity r is radius n is number of wavelengths h is planck's constant
what is a wave function?
what symbol is used for wave functions?
a mathematical way of describing the wave-like nature of an electron in three dimensions
symbol 𝛙 psi greek letter
in terms of the schrodinger equation for the hydrogen atom:
what is a Hamiltonian operator?
what is an eigenvalue?
what is an eigenfunction?
hamiltonian operator = describes a physical property of a wave
- energy, angular momentum… etc
- each property has a specific operator
eigenvalue = possible values of the property defined by the operator
eigenfunction = describes the associated energy levels
what three numbers define each solution of a wave function?
n = describes energy/size l = describes shape mL = describes orientation
what is meant by the heissenberg uncertainty principle? use waves to describe this
cannot know for sure the position and momentum of an electron
cannot have classical (“solar system”) electron orbits where momentum and position are known
we need to talk in terms of probability, which is known from the wave functions
eg in a localised wave
- continuous waves, fixed wavelength
- well defined wavelength hence well defined momentum
- frequency identified with high precision
- BUT cannot define position because its spread out
eg in a delocalised wave
- wave is localised by having lots of waves of different wavelengths
- no longer well defined momentum frequency
what is an atomic orbital and what does it describe?
atomic orbital = quantum state of an individual electron in the electron cloud around a single atom
describes the probability distribution of the electron’s position
squaring the wave function gives ?
the probability of finding an electron in any region of space
what does the radial distribution function describe?
probability of finding an electron at a certain distance from the nucleus
describes how electron density varies as a function of the radius from the nucleus
how is the RDF derived?
R(r) = radial component depends on n (principal quantum number)
R(r)^2 = probability of finding electron at fixed distance r from nucleus
electron could be found anywhere of sphere so take surface area 4𝛑r^2
multiplying probability and surface area = 4𝛑r^2•R(r)^2 = RDF
on an RDF where is there 0 probability of finding an electron?
at a radial node = radial because in all directions there is 0 probability of finding an electron
what do the peaks on an RDF graph represent?
maximum points represent the most probable distance of finding an electron from the nucleus
as the principal quantum number (n) increases what happens to the number of radial nodes on an RDF?
number of radial nodes increases
