Which one of the following elements will be an isobar of calcium if the atomic number of calcium is 20 and its mass number is 40?
Element with 22 neutrons and 18 protons
The question asks us to identify an element that is an isobar of calcium. Let's first understand what an isobar is and what information we are given about calcium.
What is an Isobar?
Isobars are atoms of different elements that have the same mass number but different atomic numbers.
The relationship between mass number (\(\text{A}\)), atomic number (\(\text{Z}\)), and the number of neutrons (\(\text{N}\)) is given by:
\(\text{A} = \text{Z} + \text{N}\)
Properties of Calcium:
We are given that calcium has an atomic number of 20 and a mass number of 40.
So, Calcium can be represented as \(^{40}_{20}\text{Ca}\).
For an element to be an isobar of calcium (\(^{40}_{20}\text{Ca}\)), it must satisfy two conditions:
Let's examine each option provided. For each option, we will calculate the atomic number (number of protons) and the mass number (number of protons + number of neutrons).
| Option | Number of Neutrons (\(\text{N}\)) | Number of Protons (\(\text{Z}\)) | Mass Number (\(\text{A} = \text{Z} + \text{N}\)) | Is it an Isobar of \(^{40}_{20}\text{Ca}\)? (A=40, Z\(\neq\)20) |
|---|---|---|---|---|
| 1 | 18 | 20 | 20 + 18 = 38 | No (\(\text{A}=38 \neq 40\)) |
| 2 | 19 | 18 | 18 + 19 = 37 | No (\(\text{A}=37 \neq 40\)) |
| 3 | 19 | 20 | 20 + 19 = 39 | No (\(\text{A}=39 \neq 40\)) |
| 4 | 22 | 18 | 18 + 22 = 40 | Yes (\(\text{A}=40\) and \(\text{Z}=18 \neq 20\)) |
Based on the analysis, the element described in option 4 has the same mass number (40) as calcium but a different atomic number (18). This fits the definition of an isobar.
| Term | Definition | Same Property | Different Property |
|---|---|---|---|
| Isotopes | Atoms of the same element | Atomic number (\(\text{Z}\), protons) | Mass number (\(\text{A}\), protons + neutrons), Neutrons (\(\text{N}\)) |
| Isobars | Atoms of different elements | Mass number (\(\text{A}\), protons + neutrons) | Atomic number (\(\text{Z}\), protons), Neutrons (\(\text{N}\)) |
| Isotones | Atoms of different elements | Neutrons (\(\text{N}\)) | Atomic number (\(\text{Z}\), protons), Mass number (\(\text{A}\), protons + neutrons) |
Atoms are made up of protons, neutrons, and electrons. Protons and neutrons are located in the nucleus and are collectively called nucleons. The number of protons determines the element (atomic number), while the total number of protons and neutrons determines the mass number. Isobars highlight that different elements can have nuclei with the same total number of particles, even though the mix of protons and neutrons is different. For example, \(^{40}_{20}\text{Ca}\) has 20 protons and 20 neutrons, while its isobar \(^{40}_{18}\text{Ar}\) has 18 protons and 22 neutrons. Both have a mass number of 40.
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