Hydrogenic Orbital

Question 1

What is a hydrogenic atom

Answer 1

Atom consisting of a single electron and a proton both of which are in motion

Question 2

Types of motion we will have

Answer 2

Translational motion of the centre of mass in space
Rotational motion of the nucleus and electron relative to the centre of mass

Question 3

reduced mass

Answer 3

the mass of two interacting bodies that can describe their inertial movement

Question 4

reduced mass equation

Answer 4

1/μ=1/m1+1/m2
μ=m1m2/m1+m2

Question 5

Simplification to reduced mass equation if m1»m2

Answer 5

μ =m1m2/m1+m2 is approx m1m2/m1 = m2

Question 6

Do we have potential energy term with our Schrodinger’s equation

Answer 6

Yes as there are charged particles

Question 7

Schrodinger’s equation

Answer 7

(-(ℏ^2)/2μ)(∇^2Ψ) + V(x)Ψ =EΨ

Question 8

Force of between charges equation

Answer 8

F=(Ze)^2/(4piE_o*r^2)
Where Z is the atomic number (number of protons and e is charge of an electron)

Question 9

Potential energy term

Answer 9

V=∫Fdr between infinity and r
V(r)=-(Ze)^2/(4piE_o*r)

Question 10

Schrodinger’s with potential energy term

Answer 10

(-(ℏ^2)/2μ)(∇^2Ψ) -(Ze)^2/(4piE_o*r) Ψ =EΨ

Question 11

Wavefunction has how many components?

Answer 11

3: r,ϕ,θ, the spherical coordinates

Question 12

Wavefunction split into functions

Answer 12

Ψ(r,ϕ,θ) =R(r)Y(ϕ,θ)=R(r)Θ(θ)Φ(ϕ)
R(r) is radial and is specified by n and l

Question 13

Why can we ignore Θ(θ)Φ(ϕ) for 1s

Answer 13

1s is symmetrical and orbital so angular components can be ignored

Question 14

Semi general wavefunction equation for Ψ_ns

Answer 14

= 1/((n^2^(n-1))(npi)^1/2)) ((Z/a_0)^(3/2)) (bracket)e^(-Zr/na_o)

Question 15

Bracket for 1s

Answer 15

1

Question 16

Bracket for 2s

Answer 16

2-Zr/a_o

Question 17

Bracket for 3s

Answer 17

27-18(Zr/a_o) + 2(Zr/a_o)^2

Question 18

What is a_o?

Answer 18

It is the bohr radius, which is equal to 52.9pm,0.529Å or 52.9*10^-12 m

Question 19

Probability density

Answer 19

Will be our wavefunction multiplied by itself which can simplify it a bit

Question 20

RDF

Answer 20

It is the radial distribution frequency, essentially the probability density multiplied by 4pi^2

Question 21

Other orbitals wavefunction

Answer 21

Some have - sign as they will have 2 regions of electron density, one where the electrons has - 1/2 spin quantum number

Question 22

Where are p, d and f orbitals in comparison to the nucleus

Answer 22

Unlike s orbitals they are excluded from the nucleus.

Question 23

What happens to the exclusion from the nucleus as l increases

Answer 23

As l increases electrons are more excluded from the nucleus