Hydrogen Atom Flashcards
(39 cards)
Balmer Series Formula
λ =(364.5nm) x (n^2 / n^2 - 4)
where n = 3,4,5…
Rydberg Formula
1/λ = Rh*(1/(n2)^2) - (1/(n1)^2)
where n1 = n2+1, n2+2, n2+3
Rh = 1.097 x 10^7 m^-1
Rydberg Ritz Combination Principle Formula
f = cRh(1/(n1)^2) - (1/(n2)^2)
Explain the Rydberg-Ritz Combination Principle
The sum or difference of certain pairs of frequencies give other frequencies that appear in the spectrum
What did the Franck Hertz Experiment prove and how
Provided direct confirmation that interal states of an atom are quanties
Using controlled energy collisions between electrons and atoms
Franck Hertz Experiment in Full
Filled a gas tube with mercury vapour at low pressure
Electrons are emitted thermally by using a filament to heat a Cathode at C
They are accelerated to the anode grid G by a potential V applied by the two electrodes
E = 1/2mv^2 = eV
Measured the electron current reaching P as a function of the accelerating voltage
Current gradually increases to begin with potential V, sudden drop in current at 4.9V, rises up again, sudden drops seen at multiples of 4.9V
Drop is due to inelastic collision between electrons and atoms in the vapour in exciting the atom from its ground state to its first excited state
Current again increases until the electron has a high enough initial energy to excite two atoms in two successive atoms. Then it is 3 atoms and so on
Explain results of Franck Hertz experiments
Accelerated electrons provide a current
Current gradually increases to begin with potential V, sudden drop in current at 4.9V, rises up again, sudden drops seen at multiples of 4.9V
Drop is due to inelastic collision between electrons and atoms in the vapour in exciting the atom from its ground state to its first excited state
Current again increases until the electron has a high enough initial energy to excite two atoms in two successive atoms. Then it is 3 atoms and so on
Quantisation of Angular Momentum
L = nℏ
nℏ = mvr
What is a stationary state
A state where the electron may exist without radiating electromagnetic radiation and classical mechanics can be used to describe the orbits
Bohr Radius
0.0529nm
(4πε0*ℏ^2)/(me^2)
Electron Energy formula in Bohr’s Planetary Model of the Atoms
En = -13.6eV * (Zeff / n)^2
Deficiencies of Bohr Model
1.No proper account of quantum mechanics
2. It is planar and the “real world” is 3-dimensional
3. It is for single electron atoms only
4. It gets the predicted angular momentum by one unit of ħ
How is an electron described as in QM and what does it disagree with
In terms of a probability density which leads to uncertainty in locating the electron
Circular orbit of Bohr’s Planetary Model
Energy of a free particle
E= ℏ^2*k^2 / 2m = p^2 / 2m
K = wave number = 2pi / lambda
p = h bar * k
What are the quantum numbers and what do they describe
n - how far the orbital is from the nucleus
l (letter between k and m) - how fast the orbit is (angular momentum)
m(l) (letter between k and m) - angle of orbit in space
m(s) - spin of the electron
Allowed value for n
1,2,3,4,5…
Allowed value for l - angular momentum
0,1,2,3,4…,(n-1)
Allowed value for m(l), magnetic quantum number
-l, -l+1,…-1,0,1,l-1,l
What are degenerate energy levels
Energy levels that have multiple solutions that correspond to the same energy, but different wavefunctions
Energy level formula
-13.6eV / n^2
How many solutions does En have
n^2 solution
If different combinations of quantum numbers lead to exactly the same energy, why list them separately?
- We find that the intensities of individual transitions between levels depend on the quantum numbers of the decaying state
- More importantly, each DIFFERENT wave function represents a very different state of motion of the electron.
If L is the angular momentum vector, then its length is given by:
|L| = √((l)(l +1)(ℏ))
Radial Probability Density Formula
P(r) dr =|Rn,l (r)|^2 (r)^2 dr
