The Shapes And Structures Of Molecules Pt. 2 Flashcards
Do electrons in atoms with more than two electrons have the same energy, how can we record how much energy is needed to remove an electron
- no they have different energies
- we can use photoelectron spectroscopy
- this bombarded a sample with x-ray photons and measuring the KE of the removed electron to tell the difference
How many electrons can an orbital hold
2 of opposite spins
What are orbitals of the same energy described as
Degenerate
What 3 things do we need to distinguish between atomic orbitals and what do we use to express these
- which ‘shell’ it is in
- whether it’s an s,p,d,f orbital
- which of the orbitals in each subshell it’s in
- each of these is expressed by a quantum number
What is the principal quantum number, what form does it take and what can it determine
The principal quantum number, n, specifies which shell is being referred to
n takes an integer value 1,2,3…
For a one electron system, n alone determines the energy of the electron
What is the angular momentum number, what form does it take
The angular momentum number, l, specifies which type of subshell orbital we are referring to (s,p,d,f…)
- l takes integer values from 0 to (n-1)
Each value of l has a different letter associated with it
Value of l: 0,1,2,3,4,5
Letter used: s,p,d,f,g,h
E.g. where n = 3, l = 0,1,2, these are s,p,d
What can the value of the angular momentum number l, take and what is the equation
The value of l determines the orbital angular momentum of the electron
Angular momentum = (h/2(pi)) sqrt(l(l+1))
Orbitals with different l numbers have different spatial arrangements
What is the magnetic quantum number
The magnetic quantum number, ml, is the number that tells us which orbital in the subshell it is
ml takes integer steps from +l to -l
E.g. for a P orbital, l = 1
So ml = -1, 0, 1
Hence there are 3 p orbitals
What is the intrinsic angular momentum, s, of all electrons
s = 1/2
what additional information/number do we need to be able to identify an individual electron in an orbital rather than simply the orbital alone
- the orientation of the electron’s intrinsic angular momentum, ms
ms = +1/2 or -1/2
for spin up (up arrow) or spin down (down arrow) respectively
what is a useful analogy for thinking about the orbital angular momentum of an electron and the intrinsic angular momentum of an electron
- we can think of the orbital angular momentum as the angular momentum the electron has due to its movement within an orbital
- we can think of the intrinsic angular momentum as the momentum an electron has due to its spin on its own axis
summarise the purpose of each of the letters when specifying the state of an electron
- n specifies the electron energy
- l specifies the magnitude of the orbital angular momentum (s,p,d etc.)
- ml specifies the orientation of the orbital angular momentum (which s,p,d orbital)
- ms specifies the orientation of the spin angular momentum (spin up or spin down)
what are two things that MUST happen when describing electrons
- in an orbital if there are two electrons they MUST have opposite spin
- any electron in an atom MUST have a unique set of 4 quantum numbers
what can the true properties of an electron be described using
a wavefunction represented by psi
what is ψ
a wavefunction, its a function of coordinates that describes the probability of finding the electron e.g. (xyz)
how do we write our wavefunction and what do the different bits represent
ψ[n,l,ml] (x,y,z)
ψ represents the wavefunction
[n,l,ml] shows that the specific function changes depending on the orbital, where our orbital is given by n,l,ml
(x,y,z) are examples of coordinates where our wavefunction is a function of coordinates
give a brief overview of the born interpretation of the wavefunction
- the wavefunction, ψ, gives numbers associated with different coordinates
- ψ ^2 or (ψ)(ψ*) gives the probability density
how can we calculate wavefunctions and energies associated with them
using the Schrodinger equation
when can we find exact solutions to the Schrodinger equation and what do these solutions represent
- we can solve Schrodinger’s equation exactly for any, one-electron system
- the solutions give the atomic orbitals
- there are a variety of solutions depending on the quantum numbers of the orbital
What is the equation for the energy, En of a wavefunction (in a one electron system)
En = (- (mee^4)/(8Eo*h^2)) (z^2/n^2)
where
me = mass of electron
e = charge on an electron
h = Planck’s constant
Eo = permittivity of free space
z = nuclear charge of atom
n = principal quantum number
this can be simplified to
En = -Rh (z^2/n^2)
where Rh = a constant
what are the key features to note about the equation for the energy of a wavefuntion
- the energy of an orbital depends on n only
- this means that 2s and 2p have the same energy, and 3s, 3p and 3d all have the same energy unless in a multi-electron system
- the predicted energies are also negative because zero energy represents an electron totally free from the nucleus
- this makes sense because as n –> infinity
En –> 0
what is a physical interpretation of the constant Rh
Rh = ionisation energy for 1H atom from 1s shell
what coordinates are usually used in the Schrodinger equation and why
- spherical polar coordinates
(r,θ,φ)
r = radius
θ = polar angle
φ = azimuthal angle - this simplifies our equation from
psi [n,l,ml] (r,θ,φ) = R [n,l] (r) x Y [l,ml] (θ, φ)
where R [n,l] (r) is the radial part of the wavefunction, dependent on n and l and defined in terms of r
and Y is the angular part of the wavefunction dependent on l and ml and defined in terms of θ and φ
what is the only factor that a 1s orbital depends on
radius, note: this is only the distance from the nucleus, it does not take into account displacement