Quantum Mechanics and Wavefunction Flashcards
What does wavefunction tell and why do we use it
It tells us how likely it is that an electron is at a particular place at a given time ( ψ or psi)
It is used because we know electrons do not have a well defined trajectory
How can you use wavefunction to work out the probability of finding a particle (Max Born)
the square of the wavefunction (ψ^2) = The probability of finding a particle in any region of space is proportional to
What did Erwin Schrodinger use wavefunction to work out
Used the concept of wavefunction to produce a mathmatical equation to calculate the behaviour of an electron (or other particle)
The allowed wavefunctions are found by solving the Schrodinger wave equation for the particle
Wavefunction can have positive and negative values, or a value of 0
When ψ = 0, what does this mean
The probability of finding an electron is 0
This is also known as a node
What is a caviat of the solutions for the Schrodinger wave equation
Solutions are only possible for certain energies
The probability density for a particle at any point is proportional to what?
The square of the wavefunction at that point
In Y1 organic chem, we are concerned about the answers that can be obtained from the Schrodingers equations in the following form:
What does R and Y stand for
R = Radial wavefunction
Y = Angular wavefunction
Each allowed solution (wavfunction) of the Schrodingers equation for the hydrogen atoms defines what?
An allowed atomic orbital
How do you convert polar coordinates (r,θ) into cartesian coordinates (x,y,z)
Polar coordinates = (R, θ)
R = radius and θ = angle measures from the x axis
x = Cos(θ) x R
y = Sin(θ) x R
How do you convert from cartesian coordinates (x,y) into polar coordinates (r,θ)
r = √x² + y²
θ = tan⁻¹ (y/x)
Solutions to the 3D schrodinger equation is describe by 3 quantum numbers
What are these
n = principle quantum number
l = orbital angular momentum quantum number
ml = magnetic quantum number
What does the Pauli exclusion principle state
No two electrons in any system can have identical values for all 4 quantum numbers
It places a restriction on the allowed values of the 4 quantum numbers
Describe the First quantum number: principle quantum number, ‘n’
It represents the energy level of the elctron (e.g. for Hydrogen this would be 1)
can have any postive integer value
Each orbital will have a ‘n’ value and the larger the value of n, the further away from the nucleus it is
What is the quantum number ‘l’
Angular momentum quantum number
Can have any value from 0 to n-1
l value describes the shape of the orbital
When l=0 we are describing an s orbital
When l=1 we are describing a p orbital (3 p orbital per energy level)
When l=2 we are describing a d orbital (5 d orbitals per energy level
If n= 3
What would the value of the quantum number l
L = 0, 1, 2
The emission spectrum of hydrogen consists of a series of lines at specific wavelengths
Rydberg developed an equation which related the wavelength of light to the transition between energy level (n)
What is this equation
λ = wavelength (m)
Rh = Rydberg’s constant = 1.097x10^7 m-1
We can consider the graphs of radial wavefunctions [R] plotted against the distance of the electron from the nucleus [r]
What does the graph look like for n=1
When radial wavefunction [R] is plotted against the distance of the electron from the nucleus [r]
What do the graphs look like for n=2
l = 0,1
What will the graphs look like when radial wavefunction [R] is plotted against distance of electron from the nucleus [r]
When n = 3
l = 0,1,2
However we are more intrested in the probability of finding the electron at a given distance from the nucleus
Hence to show the probability of finding an electron in a spherical shell at a distance [r] from the nucleus, we plot the area of a sphere against [r]
What would this look like for n=1
l = 0
For n = 2, what does the graph of the probability of finding an electron against the distance from the nucleus
l = 0, 1
for n=3, what would the graph look like when probability of finding an electron is plotted against distance from the nucleus [r]
l = 0, 1, 2
What does the shape of the s orbital look like
What does the p orbital look like in the x, y and z axis’
