Flashcards
Quantum Mechanics Calculations
Cards in this deck (33)
- 1What is de Broglie relation equation for wavelength?Wavelength = h/p =h/mv
- 2What is one Joule equal to?1Kgm^2s^-2
- 3How to convert from g to kg?multiply by 10^-3
- 4How to convert km/s to m/s?Multiply by 10^3
- 5What is one u equal to?1.6605x10^-27
- 6Why do we approximate without integrating?Because the radius
r=1.1pm is so much smaller than the Bohr radius 𝑎0=53pm, we can approximate the probability without full integration: - 7Why do we set the r as 0 in bohrs approximation?as we are at the nucleus. Therefore r=0
- 8What is the volume of a sphere?V= 4/3πr^3
- 9How do you calculate the probability that the electron will be found somewhere within a small sphere of radius 1.1 pm centred on the nucleus?The probability
P of finding the electron in a small sphere of radius r is approximately:
P≈∣ψ(0)∣^2 × volume of
the small sphere - 10How to calculate the minimum uncertainty in the speed of a ballUse the uncertainty principle
=ΔxΔp≥ 4πh
Delta P = mΔv
- 11How convert micrometer to meter?multiply by 10^-6
- 12How to calculate an energy state?En= (n^2)(h^2) / 8mL^2
Where L is equal to length of carbon bonds (calculate given internuclear distance, radius and amounts of carbon bonds)
m= mass of electron - 13How to calculate the different between two energy states?En1-n2= (n1^2-n2^2)(h^2) / 8mL^2
- 14How to calculate frequency?v = E (can be delta E)/h
- 15How to convert pm to m?x10^-12
- 16How to get mass of O2?Molecular weight of O2/ Avogadro's number = mass of O2 in grams.
- 17How to convert grams to kilograms?multiple by 10^-3
- 18What are the two lowest energy levels in any molecule?n= 1 and n=2
therefore energy state difference = 2^2 -1^2 - 19How to calculate at what value of n does the energy of the molecule reach ½kT at 300 K, and what is the separation of this level from the one immediately below?n= [kT/ 2((h^2) / 8mL^2)]^1/2
And then the lower energy level is n-1 - 20How to calculate the zero point energy of a harmonic oscillator?E0 = (0+1/2) (h with a line)(w)
where w = (k/m)^1/2 - 21What is 1N (newton) converted?1Kg m/s
- 22How to calculate the wavelength of a photon needed to excite a transition between the neighbouring energy levels of a harmonic oscillator?E delta = ℏω
That E delta = hc/ wavelength - 23How to calculate the energy and angular momentum of an electron in the highest occupied level in a particle in a ring question?To determine which is HOMO and LUMO
you need to see which state occupies both + and - ml
e.g. 18 electron
2 in 0
4 in + and - 1
4 in + and - 2
4 in + and - 3
4 in + and - 4
Therefore +/- 4 is HOMO - 24How to calculate angular momentum for a particle in a ring?Jz = mℏ
where m can be 0, +/- 1, etc - 25How to calculate the energy of a particle in a ring?Em = ℏ^2m^2/2I
Where I= mr^2 - 26How to calculate frequency?E =hv
therefore v = E/h - 27How to draw vectors?
- 28The ground-state wavefunction of a hydrogen atom is: where a0 is the Bohr radius (53 pm). At what radius does the probability of finding an electron at a point in the H atom fall to 50 per cent of its maximum value?
- 29What is the orbital angular momentum of an electron in the orbitals (a) 1s, (b) 3s, (c) 3d ? Give the numbers of angular and radial nodes in each case
- 30What are the rules to decide what transitions are allowed in the normal electronic emission spectrum of an H atom?Δl=±1
and
Δml =0,±1 - 31Calculate the ionisation energyFrom the photoelectric effect equation:
E photon=E kinetic +E binding
where:
𝐸 photon is the energy of the incoming photon,
𝐸 kinetic is the kinetic energy of the ejected electron,
𝐸 binding is the ionization energy (the energy required to remove the electron from the atom). - 32How to calculate energy of a photon?E photon = hc/λ
- 33How to calculate kinetic energy of photon?E kinetic = 1/2 (mv^2)
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- University Physical Chemistry Level 2 Flashcards on Quantum Mechanics Calculations, created by Adrianna Bialecka on 26/04/2025.
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- Adrianna Bialecka
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