Question

An isotope with mass number 44 has four more neutrons than protons. This is an isotope of what element?

Short answer

The isotope is of the element Calcium.

Step-by-step solution

Determine the relations

Given in the problem the mass number is 44 and there are four more neutrons than protons, you need to set up a system of two equations using these relationships: The total protons and neutrons equal to 44 (represented as p + n = 44); There are 4 more neutrons than protons (represented as n = p + 4).

Solve the system of equations

Substitute equation two into equation one (replace n from the first equation with p + 4), yielding p + (p + 4) = 44. This simplifies to 2p + 4 = 44 which further simplifies to 2p = 40. Dividing both sides by 2, one gets p = 20.

Find the corresponding Element

Now that we know there are 20 protons, we look at the periodic table to find the element with an atomic number of 20 which is Calcium (Ca).

Key concepts

Isotopes

Isotopes are variants of a particular chemical element that share the same number of protons but have different numbers of neutrons. This means that while they have the same atomic number, their mass number differs due to the variation in neutrons. Understanding isotopes is crucial for identifying elements and their behavior in different chemical reactions and natural processes.
For instance, carbon can exist as several isotopes: carbon-12, carbon-13, and carbon-14. Each of these has 6 protons (since it's carbon), but they have 6, 7, and 8 neutrons, respectively. Isotopes also have applications in various fields, such as radiocarbon dating in archaeology and medical diagnostics.

• Same number of protons.
• Different number of neutrons.
• Different mass numbers.

Knowing the mass number and the relationship between protons and neutrons can help identify the isotope of an element, as seen in the exercise above.

Protons and Neutrons

The atomic structure of an atom consists of a nucleus at the center surrounded by electron clouds. The nucleus itself is composed of two types of subatomic particles: protons and neutrons.
Protons bear a positive charge and determine the identity of an element. The number of protons in the nucleus defines the atomic number, which is unique for each element. Neutrons, on the other hand, are neutral particles that add mass to the atom but do not affect its chemical identity directly. They often serve to stabilize the nucleus. In the exercise, it was noted that the isotope has four more neutrons than protons, producing a mass number of 44. Calculating the exact numbers involves using the relationship between these particles:

• Protons give the element its identity.
• Neutrons contribute to isotopic variations.
• The sum of protons and neutrons equals the mass number.

Knowing these fundamentals aids in solving exercises and understanding how variations in neutron numbers result in different isotopes.

System of Equations

A system of equations is a set of two or more equations that share variables and are often solved together to find the unknown values. In the context of the exercise, creating a system of equations allows us to find the number of protons and neutrons given their relationship and the mass number.
The two key relationships are:

• The sum of protons and neutrons (p + n) equals the mass number, in this case, 44.
• The number of neutrons (n) is four more than the number of protons (p), meaning n = p + 4.

Solving these equations together involves substituting one equation into the other to eliminate a variable. This reduces complexity and allows us to solve for one variable at a time. Following these steps efficiently yields the number of protons as 20.
This approach is not just limited to chemistry; it's widely applicable in mathematics and various scientific fields where finding the precise relationship between quantities is essential.