# MCAT Physical : Periodic Trends

## Example Questions

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### Example Question #1 : Atomic Radius

Which of the given atoms has the smallest atomic radius?

P

As

Bi

N

N

Explanation:

Nitrogen, phosphorous, antimony, and bismuth are all in the same group (column) of the periodic table.

The atomic radius increases from the top of a group to the bottom, due to increased principle shell number (n). As one travels down a group, another s shell is added, meaning that electrons are added in another orbit farther from the nucleus. This serves to increase the atomic radius of the atom.

### Example Question #1 : Atomic Radius

Which of the given atoms has the largest atomic radius?

O

B

Li

Ne

Li

Explanation:

Lithium, boron, oxygen, and neon are all in the same row (period) of the periodic table.

The atomic radius decreases from left to right along a period due to increased effective nuclear force. From left to right the atomic number increases, indicating that more protons are added. The addition of protons increases the positive charge in the nucleus, pulling in the outer electrons by increasing the effective nuclear force, decreasing the radius.

In math terms, we can equate effective nuclear force using the force equation between two charged particles. We can see that the farther apart the electrons and protons are, the less the force is between them.

### Example Question #31 : Periodic Trends

Using your knowledge of periodic trends, which statement is incorrect?

Bromine has a greater electron affinity than cesium

A chloride ion has a greater atomic radius than a potassium ion

The first ionization energy of a neutral atom is always greater than the second ionization energy

Both carbon and phosphorus are less electronegative than oxygen

The atomic radius of magnesium is smaller than that of calcium

The first ionization energy of a neutral atom is always greater than the second ionization energy

Explanation:

The second ionization energy of a neutral atom is always greater than the first.

Recall that ionization energy refers to the energy required to remove an electron from an atom. The first ionization energy will result in a cation. The reduced number of electrons in a cation allows them to be pulled closer to the nucleus by the positively charged protons, effectively decreasing the atomic radius and increasing the attractive force between the electrons and the nucleus. The energy required to remove a second electron must overcome this increased affinity, and will thus be greater than the first ionization energy.

The rest of the answers can be examined with a few simple trends kept in mind. Atomic radius increases to the left of a period and down a group. If two ions have the same electron configuration (like the chlorine anion and potassium cation), then the anion will have a larger radius because it has fewer protons to draw electrons inward. Electronegativity and electron affinity increase to the right across a period and up a group.

### Example Question #1 : Atomic Radius

Which of the following would have the greatest atomic radius?

Iodine

Chlorine

Bromine

Flourine

Iodine

Explanation:

Atomic radius increases down each group of the periodic table and toward the left of each period. Since the elements listed are all in the same group, iodine would have the greatest atomic radius because it farther down the period compared to the others.

### Example Question #1 : Atomic Radius

Which of the following correctly describes the trend for atomic radius in the periodic table of elements?

Atomic radius increases with increasing energy level. Atomic radius increases as new electrons are added within the same orbital.

Atomic radius decreases with increasing energy level. Atomic radius increases as new electrons are added within the same orbital.

Atomic radius increases with increasing energy level. Atomic radius decreases as new electrons are added within the same orbital.

Atomic radius increases with increasing energy level. Atomic radius remains constant as new electrons are added within the same orbital.

Atomic radius decreases with increasing energy level. Atomic radius remains constant as new electrons are added within the same orbital.

Atomic radius increases with increasing energy level. Atomic radius decreases as new electrons are added within the same orbital.

Explanation:

Energy level increases moving down a group of the periodic table. As energy level increases, the outer valence shell becomes more distant from the nucleus, causing atomic radius to increase.

Energy level remains constant across a period, but electrons are added within the same orbitals. When new electrons are added within the same orbital, additional protons are also added to the nucleus. This increases the effective nuclear charge, pulling the electrons closer to the nucleus. The trend for atomic radius is to decrease as we move right along a row.

This means that the general trend for atomic radius is to increase as one moves to the left and downward on the periodic table.

### Example Question #1 : Electron Affinity

Electronegativity is an important concept in physical chemistry, and often used to help quantify the dipole moment of polar compounds. Polar compounds are different from those compounds that are purely nonpolar or purely ionic. An example can be seen by contrasting sodium chloride, NaCl, with an organic molecule, R-C-OH. The former is purely ionic, and the latter is polar covalent.

When comparing more than one polar covalent molecule, we use the dipole moment value to help us determine relative strength of polarity. Dipole moment, however, is dependent on the electronegativity of the atoms making up the bond. Electronegativity is a property inherent to the atom in question, whereas dipole moment is a property of the bond between them.

For example, oxygen has an electronegativity of 3.44, and hydrogen of 2.20. In other words, oxygen more strongly attracts electrons when in a bond with hydrogen. This leads to the O-H bond having a dipole moment.

When all the dipole moments of polar bonds in a molecule are summed, the molecular dipole moment results, as per the following equation.

Dipole moment = charge * separation distance

Electronegativity is associated with another function, electron affinity. What is true of electron affinity?

It is equal for sodium and for chlorine

Electron affinity is a vector quantity

It is exothermic for both chlorine and sodium

The second electron affinity is always much lower in magnitude than the first

It is endothermic for chlorine and exothermic for sodium

It is exothermic for both chlorine and sodium

Explanation:

Chlorine has a great thermodynamic desire to capture an electron, thus taking on the electronic structure of a stable noble gas. This causes chlorine to release energy when it captures an electron as it becomes more stable.

Sodium, on the other hand, would prefer to lose an electron and gain the configuration of a noble gas. Adding an electron would however award some stability to sodium, due to the complete s orbital that this would ensue.

Second electron affinity is usually encountered for such elements as oxygen and sulfur, which form anions with the addition of two electrons. The first electron affinity gives you O- or S-, and so it takes significant energy to add another electron to an already negative ion.

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