Atomic Structure

Question 1

Briefly describe the Bohr theory of the atom.

Answer 1

This theory states that:

• Electrons can only exist in fixed orbits or energy levels located at specific distances from the nucleus
• Any energy emitted or absorbed by an atom results from an electron jumping from one energy level to another

Question 2

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

Answer 2

nucleus

Note that all models assume that electrons orbit the nucleus. However, Bohr’s model is unique in that in most chemistry courses and on the MCAT, the Bohr model is usually restricted to the hydrogen atom only.

Question 3

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

Answer 3

The electron is located somewhere in a spherical probability cloud around the nucleus, called the 1s orbital.

Note that the quantum mechanical model is the one used in most chemistry courses and on the MCAT.

Question 4

An atomic electron has not absorbed any energy. Which state is it in?

Answer 4

ground state

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

Question 5

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

Answer 5

It moves into an excited state.

For example, 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 (just as one example). This state is excited, meaning that it is higher in energy than the ground state.

Question 6

What has to happen to an electron to move it from the ground state to an excited state?

Answer 6

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

The frequency of the absorbed photon corresponds to the energy difference between the two states.

Question 7

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

Answer 7

Energy is released from the atom.

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 from the atom.

Question 8

Define:

absorption spectrum

Answer 8

It is the unique set of wavelengths of light absorbed by that substance or medium.

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

Question 9

Define:

emission spectrum

Answer 9

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

The emission spectrum is displayed as a set of light lines in the spectrum, representing the emitted wavelengths. This is shown by the second bar in the image below.

Question 10

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

Answer 10

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

Both absorption and emission energy values are dependent on electrons moving between energy levels. The dark absorption line that represents jumping to a higher level should be in the exact same position as the bright emission line representing falling to a lower level; this is true because the same amount of energy is absorbed and emitted, respectively.

Question 11

What is the quantum number n called?

Answer 11

principal quantum number

It is commonly referred to as the electron’s shell.

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

Question 12

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

Answer 12

As n increases, energy increases.

Assume that the quantum number l stays constant unless told otherwise.

Question 13

What does the quantum number l represent?

Answer 13

angular momentum

(or azimuthal)

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 most chemistry courses and the MCAT will only explicitly test 0 to 3.

Question 14

In orbital theory, what do the letters s, p, d, and f indicate?

Answer 14

They 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 15

What does the quantum number m or m_l represent?

Answer 15

magnetic quantum number

It represents the orbital in which an electron exists.

m can hold any integer value between -l and +l, including 0. For example, 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 16

How many orbitals can be found in a p subshell?

Answer 16

Three orbitals:

1. p_x
2. p_y
3. p_z

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

Question 17

What does the quantum number s or m_s represent?

Answer 17

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 18

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

Answer 18

l = 0

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

Question 19

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

Answer 19

2

Note that when one orbital hold two electrons simultaneously, their spins must oppose each other.

Question 20

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

Answer 20

10

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

Question 21

What are the geometric shapes of s, p, and d orbitals, respectively?

Answer 21

• s = “spherical”
• p = “peanut”
• d = “donut”

Question 22

How many electrons exist in a filled shell with principal quantum number n?

Answer 22

2n²

For example, 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 23

How many orbitals exist per shell with respect to the principal quantum number n?

Answer 23

n²

For example, the shell n = 2 has 2² = 4 orbitals total. They are the 2s, 2p_x, 2p_y, and 2p_z orbitals.

Question 24

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

Answer 24

2(l) + 1

For example, for a d subshell (l = 2) 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 25

How many electrons can be found in the following subshells?

• s subshells
• p subshells
• d subshells
• f subshells

Answer 25

• An s subshell holds 1 x 2 = 2 electrons
• A p subshell holds 3 x 2 = 6 electrons
• A d subshell holds 5 x 2 = 10 electrons
• An f subshell holds 7 x 2 = 14 electrons

Question 26

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

Answer 26

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 #.

For example, 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. 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 27

Arrange the following subshells in terms of increasing energy:

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

Answer 27

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 28

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

p, s, f, d

Answer 28

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 29

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

For example, the 3d⁵ depiction of chromium’s valence electrons.

Answer 29

It denotes the three most important pieces of information about a subshell:
* its energy level (n)
* subshell (l)
* the total number of electrons it contains

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

Question 30

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

Answer 30

• In full spectroscopic notation:

1s²2s²2p⁶3s²3p⁶4s²

• In condensed notation:

[Ar] 4s²

Since every shell 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 fully-filled subshells up to 3p⁶.

Question 31

What does the Aufbau Principle state?

Answer 31

It 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. For example, the 1s subshell fills first, then 2s, then 2p, and so on.

Question 32

What does Hund’s rule state?

Answer 32

It describes the order of adding electrons to an unfilled subshell.

Hund’s rule explains 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 with parallel spins, until each orbital in the subshell has one electron contained within it.

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

Question 33

What does the Pauli Exclusion Principle state?

Answer 33

It states that two electrons in the same orbital must be of different spins.

As a result of this rule, no two electrons in the same atom will ever have exactly the same 4 quantum numbers (n, l, m_l, m_s).

Question 34

What types of electronic configurations lead to particularly stable atoms?

Answer 34

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, which generally remove one electron from the s subshell to give the atom a half-filled or fully-filled d subshell.

Question 35

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

Answer 35

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.

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

Question 36

Define:

effective nuclear charge

(Z_eff)

Answer 36

It is the amount of attraction that an electron in the outermost subshell has towards the positively-charged nucleus.

This number can be calculated by finding 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 outer electrons in unfilled subshells are bound to the atom.

Question 37

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

Answer 37

Z_eff(Na) = +1

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

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

Question 38

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

Answer 38

Z_eff(S) = +6

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

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