Which of the following pair of nuclides are Isobars?

Question

Prepp Team · Accepted Answer

Understanding Isobars in Nuclear Chemistry

Nuclides are atoms characterized by their atomic number (the number of protons in the nucleus) and their mass number (the total number of protons and neutrons). Different types of nuclides exist, including isotopes, isobars, isotones, and isomers. This question focuses on identifying a pair of isobars from the given options.

What are Isobars?

Isobars are defined as nuclides of different chemical elements that have the same mass number ($A$) but different atomic numbers ($Z$). Since they have different atomic numbers, they have a different number of protons and thus are atoms of different elements.

The notation for a nuclide is typically $^{A}_{Z}X$, where:

$X$ is the chemical symbol of the element.
$A$ is the mass number (number of protons + neutrons).
$Z$ is the atomic number (number of protons).

For two nuclides to be isobars, their $A$ values must be equal, and their $Z$ values must be different.

Analyzing the Given Pairs of Nuclides

Let's examine each pair of nuclides provided in the options to determine their mass numbers ($A$) and atomic numbers ($Z$) and check if they fit the definition of isobars.

Option 1: $ ^{2}_{1}H, \, ^{3}_{1}H $

For $ ^{2}_{1}H $: $A = 2$, $Z = 1$.
For $ ^{3}_{1}H $: $A = 3$, $Z = 1$.

In this pair, the atomic numbers ($Z$) are the same ($Z=1$), but the mass numbers ($A$) are different ($A=2$ and $A=3$). Nuclides with the same atomic number but different mass numbers are called isotopes. Therefore, this pair is not a pair of isobars.

Option 2: $ ^{3}_{1}H, \, ^{3}_{2}He $

For $ ^{3}_{1}H $: $A = 3$, $Z = 1$.
For $ ^{3}_{2}He $: $A = 3$, $Z = 2$.

In this pair, the mass numbers ($A$) are the same ($A=3$), but the atomic numbers ($Z$) are different ($Z=1$ and $Z=2$). The different atomic numbers mean they are different elements (Hydrogen, H, and Helium, He). This pair perfectly matches the definition of isobars. $^{3}_{1}H$ is also known as Tritium, an isotope of Hydrogen, and $^{3}_{2}He$ is an isotope of Helium.

Option 3: $ ^{198}_{80}Hg, \, ^{179}_{79}Au $

For $ ^{198}_{80}Hg $: $A = 198$, $Z = 80$.
For $ ^{179}_{79}Au $: $A = 179$, $Z = 79$.

In this pair, both the mass numbers ($A$) and the atomic numbers ($Z$) are different. Therefore, this pair is neither isobars nor isotopes (or isotones, or isomers).

Option 4: $ ^{1}_{1}H, \, ^{3}_{1}H $

For $ ^{1}_{1}H $: $A = 1$, $Z = 1$.
For $ ^{3}_{1}H $: $A = 3$, $Z = 1$.

In this pair, the atomic numbers ($Z$) are the same ($Z=1$), but the mass numbers ($A$) are different ($A=1$ and $A=3$). Similar to Option 1, these are isotopes of Hydrogen. $^{1}_{1}H$ is also known as Protium, and $^{3}_{1}H$ is Tritium. This pair is not a pair of isobars.

Summary of Analysis

We can summarize the properties of each pair in a table:

Pair of Nuclides	Nuclide 1 ($^{A}_{Z}X$)	A1	Z1	Nuclide 2 ($^{A}_{Z}X$)	A2	Z2	Relationship (A, Z comparison)	Type
Option 1	$ ^{2}_{1}H $	2	1	$ ^{3}_{1}H $	3	1	A1 ≠ A2, Z1 = Z2	Isotopes
Option 2	$ ^{3}_{1}H $	3	1	$ ^{3}_{2}He $	3	2	A1 = A2, Z1 ≠ Z2	Isobars
Option 3	$ ^{198}_{80}Hg $	198	80	$ ^{179}_{79}Au $	179	79	A1 ≠ A2, Z1 ≠ Z2	Neither
Option 4	$ ^{1}_{1}H $	1	1	$ ^{3}_{1}H $	3	1	A1 ≠ A2, Z1 = Z2	Isotopes

Based on the analysis, only the pair $ ^{3}_{1}H, \, ^{3}_{2}He $ has the same mass number ($A=3$) and different atomic numbers ($Z=1$ and $Z=2$). Therefore, this pair represents isobars.

Conclusion

The pair of nuclides that are isobars is $ ^{3}_{1}H, \, ^{3}_{2}He $.

Revision Table: Nuclide Relationships

Term	Definition	Comparison (A, Z, N)	Example
Isotopes	Nuclides of the same element (same Z) with different numbers of neutrons (different A).	Same Z, Different A, Different N	$ ^{1}_{1}H $, $ ^{2}_{1}H $, $ ^{3}_{1}H $
Isobars	Nuclides of different elements (different Z) with the same mass number (same A).	Same A, Different Z, Different N	$ ^{3}_{1}H $, $ ^{3}_{2}He $
Isotones	Nuclides with the same number of neutrons (same N), but different atomic numbers (different Z) and different mass numbers (different A). Note: $N = A - Z$.	Same N, Different A, Different Z	$ ^{3}_{1}H $ (N=2), $ ^{4}_{2}He $ (N=2)
Isomers	Nuclides with the same atomic number (Z) and mass number (A), but in different nuclear energy states. Often denoted by 'm' (metastable).	Same A, Same Z, Same N (Different energy state)	$ ^{99}_{43}Tc $, $ ^{99m}_{43}Tc $

Additional Information: Properties of Isobars

While isobars have the same mass number, their chemical properties are different because chemical properties are determined by the number of electrons, which in a neutral atom is equal to the atomic number ($Z$). Since isobars have different $Z$, they belong to different elements and therefore have different chemical behaviors.

Their physical properties, such as atomic mass (which is approximately equal to the mass number), can be similar, but other physical properties like density, melting point, etc., will differ due to their different electronic structures and nuclear compositions (different numbers of protons and neutrons, even if the sum is the same).

Isobars are often studied in nuclear physics and chemistry as they relate to radioactive decay processes, such as beta decay, where a nucleus can transform into an isobar by changing a neutron into a proton or vice versa, keeping the mass number constant.

Prepp Team · Answer

$ ^{2}_{1}H, \, ^{3}_{1}H $

Prepp Team · Answer

$ ^{198}_{80}Hg, \, ^{179}_{79}Au $

Prepp Team · Answer

$ ^{1}_{1}H, \, ^{3}_{1}H $

Understanding Isobars in Nuclear Chemistry

What are Isobars?

Analyzing the Given Pairs of Nuclides

Option 1: \( ^{2}_{1}H, \, ^{3}_{1}H \)

Option 2: \( ^{3}_{1}H, \, ^{3}_{2}He \)

Option 3: \( ^{198}_{80}Hg, \, ^{179}_{79}Au \)

Option 4: \( ^{1}_{1}H, \, ^{3}_{1}H \)

Summary of Analysis

Conclusion

Revision Table: Nuclide Relationships

Additional Information: Properties of Isobars

Important Questions from Nuclei

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Pair of Nuclides	Nuclide 1 (\(^{A}_{Z}X\))	A1	Z1	Nuclide 2 (\(^{A}_{Z}X\))	A2	Z2	Relationship (A, Z comparison)	Type
Option 1	\( ^{2}_{1}H \)	2	1	\( ^{3}_{1}H \)	3	1	A1 ≠ A2, Z1 = Z2	Isotopes
Option 2	\( ^{3}_{1}H \)	3	1	\( ^{3}_{2}He \)	3	2	A1 = A2, Z1 ≠ Z2	Isobars
Option 3	\( ^{198}_{80}Hg \)	198	80	\( ^{179}_{79}Au \)	179	79	A1 ≠ A2, Z1 ≠ Z2	Neither
Option 4	\( ^{1}_{1}H \)	1	1	\( ^{3}_{1}H \)	3	1	A1 ≠ A2, Z1 = Z2	Isotopes