Electronic Structure

Question 2

Briefly describe the Bohr Theory of the atom.

Answer 2

• Electrons can only exist in fixed orbits or energy levels.
• These energy levels are at specific distances from the nucleus.
• Any energy emitted/absorbed from/by an atom would be the result of an electron jumping from one enevrgy level to another.

Question 3

In the Bohr Model, what does the Hydrogen electron orbit?

Answer 3

The electron orbits the nucleus.

Note: all models assume that electrons orbit the nucleus, but Bohr’s model is unique in that on the MCAT, the Bohr model is usually restricted to the hydrogen atom only.

Question 4

In the quantum mechanical model, where does the Hydrogen electron exist?

Answer 4

In a spherical probability cloud around the nucleus, called the 1s orbital.

Note: the quantum mechanical model is the one that we use on the MCAT by default.

Question 5

In which state do atomic electrons exist, if they have not absorbed any energy?

Answer 5

The ground state.

The ground state is the lowest possible energy orbital that any atomic electron may occupy.

Question 6

When a ground state Hydrogen electron absorbs energy, what happens to it?

Answer 6

The electron moves into an excited state.

Ex: a ground-state electron in Hydrogen is in the 1s state. If it absorbs the right amount of energy, it can jump into the 3p state, which is excited (higher) in energy than the ground state.

Question 7

What has to happen to an electron in order for it to change from the ground state to an excited state?

Answer 7

The electron must absorb energy, typically in the form of a photon, to go from the ground state to an excited state.

Question 8

What direction does energy flow when an atomic electron drops from the excited state back to the ground state?

Answer 8

Energy is released.

Since the ground state is lower in energy than the excited state, the change from excited to ground is always accompanied by a release of energy.

Question 9

Define:

Absorption spectrum

Answer 9

The unique set of wavelengths of light absorbed by a specific substance or medium.

The absorption spectrum is typically displayed as a set of dark lines (or missing lines) in the spectrum, representing the absorbed wavelengths. This is the third bar in the image.

Question 10

Define:

Emission spectrum

Answer 10

The unique spectrum of bright lines or bands of light emitted by a particular substance when it is electronically excited.

This is the second bar in the image.

Question 11

How do a substance’s absorbtion and emission spectral lines compare to one another?

Answer 11

The absorbtion and emission spectral lines will overlap one another perfectly.

Both absorbtion and emission energy values are dependent on electrons moving between energy levels. Jumping to a higher level (dark absorption line) should be in the exact same position as jumping to a lower level (bright emission line) since it’s the exact same amount of energy absorbed and emitted, respectively.

Question 13

What does the letter n define?

Answer 13

n is the principal quantum number, and is commonly referred to as the shell the electron is in.

n can have any whole number value greater than or equal to 1.

Question 14

As the principle quantum number n increases, what happens to the energy?

Answer 14

As n increases, energy increases.

Remember: assume that the quantum number l stays constant unless told otherwise on the MCAT.

Question 15

What is the quantum number l called?

What does it represent?

Answer 15

l is the angular momentum (or azimuthal) number.

It represents an electron’s subshell.

If l = 0, the electron is in an s subshell.
If l = 1, the electron is in a p subshell.
If l = 2, the electron is in a d subshell.
If l = 3, the electron is in a f subshell.

l can take any integer value from 0 to n - 1, but on the MCAT it will vary from 0 to 3.

Question 16

In quantum mechanics, what are s, p, d, and f?

How are these values determined?

Answer 16

The letters s, p, d, f symbolize the subshells in which an electron can exist.

The value of the quantum number l determines the subshell. s, p, d, and f subshells correspond to l = 0, 1, 2, and 3, respectively.

Question 17

What is the quantum number m or *m_l *called?

What does it represent?

Answer 17

m or m_<em>l</em>is the magnetic quantum number.

It represents the orbital in which an electron exists.

m can hold any integer value between -l and +l, including 0.

Ex: for an electron whose l = 1 (p subshell), m can equal -1, 0, or 1. These values correspond to the p_x, p_y, and p_z orbitals, respectively.

Question 18

How many orbitals can be found in a p subshell?

Answer 18

A p subshell has three orbitals: p_x, p_y, and p_z.

Remember: l = 1 for any p subshell. m_l can range from -l to l, or -1, 0, or 1 in a p subshell. These values correspond to the x, y, and z orbitals.

Question 19

What is the quantum number *s** or m_s *called?

What does it represent?

Answer 19

s or m_sis the spin quantum number.

It represents the spin direction of an electron.

s can have exactly one of two values, +1/2 and -1/2, corresponding to spin-up and spin-down. These two values are inherently equal in energy.

Question 20

What is the value of l for any electron in an s orbital?

Answer 20

For any s electron, l = 0.

l can range from any value from 0 to n-1, and determines the subshell. By definition, if l = 0 for an electron, that electron exists in an s orbital.

Question 21

What is the maximum number of electrons found in an orbital?

Answer 21

Each orbital can hold up to 2 electrons.

Note: When one orbital hold two electrons simultaneously, one must be spin-up and the other spin-down.

Question 22

With 5 orbitals, how many electrons can a d subshell hold?

Answer 22

A d subshell holds up to 10 electrons.

Each of the 5 orbitals can have 1 spin-up electron and 1 spin-down, for a total of 2(5)=10 total.

Question 23

What are the geometric shapes of:

• s orbitals?
• p orbitals?
• d orbitals?

Answer 23

• s = ‘spherical’
• p = ‘peanut’
• d = ‘donut’

Question 24

How many orbitals are there per shell with principal quantum number n?

Answer 24

A shell will have n² orbitals.

Ex: For the shell *n *= 2 there are 2² = 4 orbitals total. They are the 2s, 2p_x, 2p_y, and 2p_z orbitals.

Question 25

How many electrons are there in a shell with principal quantum number n?

Answer 25

There are 2n² electrons in the shell.

Ex: For the n = 2 shell:

2(2²) = 8

This shell has 4 orbitals: 2s, 2p_x, 2p_y, 2p_z. Each of those can hold 2 electrons, for a total of 8 in the shell.

Question 26

How many orbitals are there per subshell with azimuthal quantum number l?

Answer 26

A subshell will have 2(l) + 1 orbitals.

Ex: For a d subshell, *l *= 2, and there are 2(2) + 1 = 5 orbitals total. They are the d_xy, d_xz, d_yz, d_x²_-y², and d_z² orbitals.

Question 27

How many electrons can be found in a:

s subshell?
p subshell?
d subshell?
f subshell?

Answer 27

An s subshell holds 1x2=2 electrons.

A p subshell holds 3x2=6 electrons.

A d subshell holds 5x2=10 electrons.

An f subshell holds 7x2=14 electrons.

Question 28

Given two specific subshells, what determines which one will fill with electrons first?

Answer 28

The subshell with the lowest total energy will fill first.

Total energy can be approximated as E=n+l, where n=principal quantum # and l=azimuthal quantum #.

Ex: For a 4s subshell, n = 4 and l = 0, so n+l = 4. So a 4s subshell will fill before a 3d subshell, which has n = 3, l = 2, and n+l = 5.

Note: in the case of a tie between two subshells with the same n+l value, the one with the lower n will fill first.

Question 29

Arrange the following subshells in terms of increasing energy:

4s, 6s, 3d, 2s, 4f

Answer 29

In order of increasing energy:

2s < 4s < 3d < 6s < 4f

The total order of all relevant subshells in the full Periodic Table is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d

Question 30

For a given value of n, please rank the following subshells in order of increasing energy:

p, s, f, d

Answer 30

In order of increasing energy:

s < p < d < f

These subshells differ in their value of l. For a given n, the higher the l, the higher the energy.

Question 31

Explain each of the 3 terms for the spectroscopic notation for an atom’s electronic structure?

Ex: the 3d⁵ depiction of Chromium’s valence electrons.

Answer 31

The spectroscopic notation denotes the three most important pieces of information about a subshell: its energy level (n), subshell (l), and the total number of electrons it contains.

So Chromium’s 3d⁵ explains that there are 5 valence electrons, with n = 3 and l = 2.

Question 32

Give both the full and condensed form of the spectroscopic notation for Calcium (Ca).

Answer 32

Full: 1s²2s²2p⁶3s²3p⁶4s²

Condensed: [Ar] 4s²

Since every up to 3p⁶ is completely filled, they are not chemically relevant - only valence electrons participate in chemical reactions. Therefore, they can all be abbreviated as the Noble Gas from the previous row, in this case Ar, which represents the element with full-filled subshells up to 3p⁶.

Question 33

Define:

The Aufbau Principle

Answer 33

The Aufbau Principle describes the order in which subshells are filled with electrons as atomic number increases. Aufbau is German for ‘Building Up’.

Shells/subshells of lower energy get filled with electrons before higher energy shells/subshells.

Ex: The 1s subshell fills first, then 2s, then 2p, and so on.

Question 34

Define:

Hund’s Rules

Answer 34

Hund’s Rules (a.k.a. the stinky bus rules), describe the order of adding electrons to an unfilled subshell.

Hund’s Rules explain that when electrons are added to a subshell that has more than 1 orbital (p, d, or f), each orbital first receives a single electron, each spin-up, until each orbital in the subshell has one electron contained within it.

Only once the orbital is half full will spin-down electrons be added, one per orbital, until the subshell is completely filled.

Question 35

Define:

The Pauli Exclusion Principle

Answer 35

The Pauli Exclusion Principle states that two electrons in the same orbital must be of different spins.

The result of this rule is that two electrons in the same atom will never have exactly the same 4 quantum numbers (n, l, m_l, m_s).

Question 36

What types of electronic configurations lead to particularly stable atoms?

Answer 36

Fully-filled and half-filled subshells make atoms particularly stable.

In particular, atoms with p3, p6, d5, and d10 valence shell configurations are especially stable.

A classic MCAT question will ask about exceptions to typical stability trends, and the answer will be due to an atom have a half-filled subshell.

Question 37

Use electronic structure to explain the difference in stability between atomic Phosphorus (P) and Sulfur (S).

Answer 37

Phosphorus’ valence shell configuration is 3p³, while Sulfur’s is 3p⁴.The p-block electrons around Phosphorus will therefore be more stable, as the p subshell is half-filled with parallel-spin electrons, a particularly stable configuration.

Sulphur will be slightly less stable, as its p subshell contains one additional electron paired in an orbital with an anti-parallel spin electron.

Question 38

Define and explain how to calculate:

Effective Nuclear Charge Z_eff

Answer 38

The effective nuclear charge is the amount of attraction that an electron in the outermost subshell has towards the positively-charged nucleus.

This number can be calculated by calculating the positive charge of the nucleus and subtracting the total number of shielding electrons in the inner, fully-filled subshells.

The higher the Z_eff, the more strongly the valence electrons are bound to the atom.

Question 39

What is the effective nuclear charge (Z_eff) for atomic Na?

Answer 39

Z_eff (Na) = +1.

Na has 11 total protons in the nucleus, and 10 total electrons in inner subshells (1s²,2s², 2p⁶), so:

Z_eff(Na) = +11 - 10 = +1

Question 40

What is the effective nuclear charge (Z_eff) for atomic S?

Answer 40

Z_eff (S) = +6.

S has 16 total protons in the nucleus, and 10 total electrons in inner subshells (1s²,2s², 2p⁶), so:

Z_eff(S) = +16 - 10 = +6