Give the nuclear symbol for the isotope of gallium

Give the nuclear symbol for the isotope of gallium, Ga, that contains 40 neutrons per atom.

The correct answer and explanation is :

The nuclear symbol for the isotope of gallium (Ga) that contains 40 neutrons is written as:

$$
^{69}_{31} \text{Ga}
$$

Explanation:

1. Understanding the Nuclear Symbol:
   The nuclear symbol $^{A}_{Z} \text{X}$ represents an isotope of an element, where:

• $X$ is the chemical symbol of the element (in this case, “Ga” for gallium).
• $Z$ is the atomic number, which represents the number of protons in the nucleus of the atom.
• $A$ is the mass number, which is the total number of protons and neutrons in the nucleus.

1. Gallium and its Atomic Number:
   Gallium (Ga) has an atomic number of 31, which means every gallium atom has 31 protons in its nucleus. This value is constant for all isotopes of gallium.
2. Determining the Mass Number:
   The number of neutrons in an atom is determined by subtracting the number of protons (the atomic number) from the mass number (the total number of protons and neutrons). In this case, we are told that the isotope of gallium has 40 neutrons. $$
   \text{Mass Number (A)} = \text{Number of Protons (Z)} + \text{Number of Neutrons}
   $$ $$
   A = 31 + 40 = 71
   $$ Therefore, the mass number for this isotope is 71.
3. Conclusion:
   The isotope of gallium with 40 neutrons per atom has the mass number of 71, so its nuclear symbol is $^{71}_{31} \text{Ga}$.
4. Isotope Notation:
   This notation helps distinguish different isotopes of an element. The number of protons (31 for gallium) is fixed, but the number of neutrons can vary. This gives rise to different isotopes with the same chemical properties but slightly different physical properties (such as mass and stability).