Question

An ion having a $4+$ charge and a mass of 49.9 u has 2 electrons with principal quantum number $n=1,8$ electrons with $n=2$ and 10 electrons with $n=3.$ Supply as many of the properties for the ion as possible from the information given. (Hint: In forming ions for this species, the 4$s$ electrons are lost before the 3$d$ electrons.) a. the atomic number b. total number of $s$ electrons c. total number of $p$ electrons d. total number of $d$ electrons e. the number of neutrons in the nucleus f. the ground-state electron configuration of the neutral atom

Short answer

The short answer to the question: a. The atomic number is 16. b. The total number of s electrons is 4. c. The total number of p electrons is 16. d. There are no d electrons present in the ion. e. The number of neutrons in the nucleus is 34. f. The ground-state electron configuration of the neutral atom is 1s² 2s² 2p⁶ 3s² 3p⁴.

Step-by-step solution

a. the atomic number

Since we know that the ion has a $4+$ charge and the total number of electrons, we can find the number of protons, which is the atomic number of the element. The total number of electrons in the ion is 2 (in n=1) + 8 (in n=2) + 10 (in n=3) = 20 electrons. Accounting for the $4+$ charge, we have 20 electrons - 4 = 16 protons. So, the atomic number is 16.

b. Total number of $s$ electrons

To find the total number of $s$ electrons, we consider the hint saying that the 4s electrons are lost before the 3d electrons while forming ions. In this ion, two 4s electrons were lost. Hence, the total number of $s$ electrons in the ion is 2 (from n=1) + 2 (from n=3) = 4 $s$ electrons.

c. Total number of $p$ electrons

In the second energy level (n=2), there are 8 electrons. As there are no $s$ electrons for n=2, then all of these 8 electrons are $p$ electrons. In the third level (n=3), 2 electrons are in the 3s orbital, so the remaining 8 electrons are $p$ electrons. So, the total number of $p$ electrons is 8 (from n=2) + 8 (from n=3) = 16 $p$ electrons.

d. Total number of $d$ electrons

We are given the hint that 4s electrons are lost before 3d electrons. Hence, there are no $d$ electrons in this ion, as they would have been removed if they existed.

e. The number of neutrons in the nucleus

We are given the mass number (49.9 u, which we can round to 50). We can then use this information along with the atomic number, 16, to find the number of neutrons in the nucleus. The mass number is the sum of the protons and neutrons; thus, the number of neutrons is 50 - 16 = 34 neutrons.

f. The ground-state electron configuration of the neutral atom

For the ground state electron configuration of the neutral atom, we have to know the number of electrons in the neutral atom. In this case, it's the same as the atomic number, which is 16. The ground-state electron configuration follows the order: 1s² 2s² 2p⁶ 3s² 3p⁴.

Key concepts

Atomic Number

The atomic number is a fundamental property of an element. It tells us the number of protons in the nucleus of an atom. Each element has a unique atomic number that defines its identity. For example, if an atom has 16 protons, it means its atomic number is 16, and it represents sulfur on the periodic table.
In the given exercise, we determine the atomic number by analyzing the number of electrons in the ion and considering its charge. The ion has a 4+ charge and a total of 20 electrons. Since the ionic charge is positive, we add the charge number to the electrons to find the atomic number. Therefore, 20 (electrons) - 4 = 16 (protons), meaning the atomic number is 16.

Principal Quantum Number

The principal quantum number, denoted as 'n', signifies the major energy level of an electron within an atom. It is an integer value that also determines the size and energy of an electron's orbit.

• When n = 1, electrons are in the first energy level, closest to the nucleus.
• When n = 2, the electrons are in the second energy level, a bit farther from the nucleus with higher energy.
• When n = 3, they are in the third energy level, and so on.

In this problem, we observe that the ion has electrons in the n=1, n=2, and n=3 levels. The distribution of electrons across these energy levels gives insights into the element’s electron configuration and stability.

Neutrons

Neutrons are neutrally charged particles located in the nucleus of an atom. They don't affect the charge but play a crucial role in the atomic mass and stability of the nucleus.
To find the number of neutrons, we subtract the atomic number from the mass number: the total number of protons plus neutrons.
In the example given, the mass number is roughly 50, with an atomic number of 16. Therefore, the number of neutrons is calculated as 50 (mass number) - 16 (atomic number) = 34 neutrons.

Ion Charge

Ion charge is the difference between the number of protons and electrons in an atom. This difference results in an atom having either a positive or negative charge.
A positive ion (cation) forms when an atom loses electrons, while a negative ion (anion) forms when an atom gains electrons. For instance, an ion with a 4+ charge indicates it has lost 4 electrons relative to its neutral state.

• If the neutral atom had 20 electrons initially, losing 4 leaves the ion with 16 electrons.
• The charge gives us a clue about which electrons might have been lost, often starting with those in the outermost energy levels.

Understanding ion charge is important for predicting chemical behavior and reactivity of elements.