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Chemistry > Atomic Orbitals > Flashcards

Atomic Orbitals Flashcards

1
Q

How can p orbitals be described in terms of energy, given that they have the same energy?

A

Degenerate.

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2
Q

What is meant by saying that d orbitals have 5-fold degeneracy?

A

All five d orbitals in the same shell have the same energy.

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3
Q

What values can the principle quantum number, n, take?

A

Integer values.

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4
Q

In a one electron system what is the value of n alone responsible for describing?

A

The energy of the electron.

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5
Q

What values can the angular momentum quantum number, l, take?

A

n-1.

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6
Q

What is the equation for angular momentum?

A

(h/2π) x sqrt(lx(l+1))

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7
Q

What letter corresponds with l=0

A

s

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8
Q

What letter corresponds with l=1

A

p

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9
Q

What letter corresponds with l=2

A

d

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10
Q

What letter corresponds with l=3

A

f

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11
Q

What letter corresponds with l=4

A

g

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12
Q

What letter corresponds with l=5

A

h

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13
Q

What values can the magnetic quantum number, m_l, take?

A

From -l to +l.

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14
Q

What does the magnetic quantum number describe?

A

The orientation of the orbital’s angular momentum.

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15
Q

What does the angular momentum quantum number describe?

A

The magnitude of the orbital’s angular momentum.

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16
Q

As well as the three quantum numbers, what other value can be used to describe an electron?

A

Spin.

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17
Q

What is the fixed value of spin for an electron?

A

1/2

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18
Q

What does m_s define?

A

The alignment of an electron’s spin.

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19
Q

What is the symbol for wavefunction?

A

Psi.

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20
Q

Psi squared gives you what?

A

A probability density - a measure of the probability of finding an electron at a given position.

21
Q

For what systems is it possible to solve the Schrödinger equation exactly, giving atomic orbitals?

A

One electron systems.

22
Q

What is the equation for the energy of a wavefunction?

A

E_n= -((m_e x e^4)/(8ε_o x h^2)) x (z^2/n^2)

Where m_e = mass of the electron
ε_o = vacuum permittivity.
e=elementary charge
z= nuclear charge.

23
Q

Why is the equation for energy of a wavefunction only dependent on n?

A

It is for a one-electron system, so energy is only dependent on n.

24
Q

The constants in the equation for the energy of a wavefunction can be grouped to give what constant? What does the equation simplify to?

A

The Rydberg Constant (R_H).

R_H x (z^2/n^2)

25
Q

What is an important point about the results of the Schrödinger equation?

A

The energies are negative, and tend towards zero the larger n gets.

26
Q

In terms of the Schrödinger equation, what is the ionisation energy?

A

The energy required to promote an electron from the lowest energy level to zero energy.

27
Q

Should Polar or Cartesian coordinates be used to describe the position of an electron?

A

Polar

28
Q

What values can the angle θ take?

A

From 0 to π (180 degrees).

29
Q

What values can the angle φ take?

A

From 0 to 2π (360 degrees).

30
Q

What diagram can be used to show how the wavefunction varies with different values of θ and φ?

A

3D isosurface plots.

31
Q

What is a disadvantage of 3D isosurface plots?

A

Do not give a measure of the probability of finding an electron in a given position.

32
Q

What do the contours join up in a contour plot?

A

Areas of equal values of wavefunction (psi).

33
Q

Does a density plot show the probability of finding an electron at a given position, and if so how?

A

Yes. The darker it is, the higher the value of psi and the higher the probability of finding an electron at that point.

34
Q

What is the Radial Distribution Function (RDF)?

A

The sum of the electron density in a thin shell at a set distance, r, from the nucleus.

35
Q

What information is given by the RDF?

A

The probability of finding an electron in a thin shell of thickness δr, at radius r from the nucleus.

36
Q

What is RDF the product of?

A

ψ^2 x r^2.

37
Q

What is the Bohr radius (a_0)?

A

The radius at which the electron is most likely to be found.

38
Q

How can the number of radial nodes be calculated?

A

n-1-l

39
Q

How can the number of angular nodes be calculated?

A

It is equal to l

40
Q

How can the total number of nodes be calculated?

A

n-1

41
Q

What is unusual about the 3d_z^2 orbital’s angular node?

A

It is a nodal cone rather than a nodal plane.

42
Q

Why is the orbital approximation used rather than the Schrödinger equation for multi-electron systems?

A

Repulsion between electrons is an extra factor that must be taken into account, so the Schrödinger equation can’t be solved exactly.

43
Q

What assumptions are made in the orbital approximation?

A

From the point of view of one electron, the effect of all the other electrons can be averaged out to give a modified potential that is spherically symmetrical and centred on the nucleus.

44
Q

As a result pf screening, what is the effective nuclear charge (z_eff) for electrons in the 1s orbital?

A

About 2.7

45
Q

As a result pf screening, what is the effective nuclear charge (z_eff) for electrons in the 2s orbital?

A

About 1.3

46
Q

By what percentage of the charge of a proton do electrons in the 1s orbital screen each other by?

A

30%

47
Q

Explain why the 2s orbital is lower in energy than the 2p orbital?

A

It penetrates the 1s orbital to a greater extent than the 2p orbital on a graph of RDF.

48
Q

Why is the 4s orbital lower in energy than the 3d orbital in many multi-electron systems?

A

Greater nuclear charge contracts the orbitals so the 4s orbital penetrates lower orbitals to a sufficient extent that, on average, the electrons in this orbital experience greater effective nuclear charge than those in the 3d orbital.

Chemistry (9 decks)

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