Gallium (Ga) consists of two naturally occurring isotopes with masses of 68.926 and 70.925 amu. a. How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. b. The average atomic mass of Ga is 69.72 amu. Calculate the abundance of each isotope.

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Step 1: Determine the number of protons in each isotope of Gallium. Since Gallium (Ga) has an atomic number of 31, each isotope has 31 protons.

Step 2: Calculate the number of neutrons in each isotope. For the isotope with a mass of 68.926 amu, subtract the number of protons (31) from the mass number (69) to get the number of neutrons. Similarly, for the isotope with a mass of 70.925 amu, subtract the number of protons (31) from the mass number (71).

Step 3: Write the complete atomic symbol for each isotope. The atomic symbol is written as \( ^A_Z \text{X} \), where \( A \) is the mass number, \( Z \) is the atomic number, and \( \text{X} \) is the element symbol. For Gallium, the symbols are \( ^{69}_{31}\text{Ga} \) and \( ^{71}_{31}\text{Ga} \).

Step 4: Set up the equation for the average atomic mass of Gallium using the formula: \( \text{Average atomic mass} = (\text{mass of isotope 1} \times \text{abundance of isotope 1}) + (\text{mass of isotope 2} \times \text{abundance of isotope 2}) \). Let \( x \) be the abundance of the first isotope, then \( 1-x \) is the abundance of the second isotope.

Step 5: Substitute the given values into the equation: \( 69.72 = (68.926 \times x) + (70.925 \times (1-x)) \). Solve for \( x \) to find the abundance of the first isotope, and use \( 1-x \) to find the abundance of the second isotope.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different mass numbers. For gallium, the two isotopes mentioned have masses of 68.926 amu and 70.925 amu, indicating they have the same atomic number (31 protons) but differ in neutron count (37 and 39 neutrons, respectively).

Atomic Symbol

The atomic symbol of an element is a notation that represents the element's identity, including its atomic number (number of protons) and mass number (total number of protons and neutrons). For gallium isotopes, the complete atomic symbols would be written as 68Ga and 70Ga, where 'Ga' is the chemical symbol for gallium, '68' and '70' represent the mass numbers.

Average Atomic Mass and Abundance

The average atomic mass of an element is a weighted average of the masses of its isotopes, taking into account their relative abundances. To calculate the abundance of each isotope, one can set up equations based on the average atomic mass and the known masses of the isotopes, allowing for the determination of the percentage of each isotope present in nature.

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