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Let's break down the information from the table to solve the given problems.

### a) **Calculating the average atomic mass of nickel**

The average atomic mass of an element is calculated using the weighted average of its isotopes based on their relative abundances. The formula is:

\[
\text{Average Atomic Mass} = \sum (\text{Isotope Mass} \times \text{Abundance Fraction})
\]

From the table, we have the following isotopes with their masses and abundances:
- \( ^{58}\text{Ni} \): Mass = 57.935 amu, Abundance = 68.077%
- \( ^{60}\text{Ni} \): Mass = 59.931 amu, Abundance = 26.223%
- \( ^{61}\text{Ni} \): Mass = 60.936 amu, Abundance = 1.14%
- \( ^{62}\text{Ni} \): Mass = 61.928 amu, Abundance = 3.634%
- \( ^{64}\text{Ni} \): Mass = 63.928 amu, Abundance = 0.926%

We'll convert the percentages to fractions (divide by 100) and apply the formula.

### b) **Determining the number of neutrons in each isotope**

To find the number of neutrons in each isotope, use the formula:

\[
\text{Number of Neutrons} = \text{Mass Number} - \text{Atomic Number}
\]

For nickel, the atomic number is 28 (since nickel has 28 protons).

The mass number for each isotope corresponds to the number written in the superscript (e.g., 58 for \(^{58}\text{Ni}\)).

Let's calculate both parts. I'll start with the average atomic mass in part (a).### a) The average atomic mass of nickel is approximately **58.693 amu**.

### b) Now let's calculate the number of neutrons for each isotope of nickel. The atomic number of nickel is 28. Therefore, for each isotope:

- \( ^{58}\text{Ni} \): Number of neutrons = 58 - 28
- \( ^{60}\text{Ni} \): Number of neutrons = 60 - 28
- \( ^{61}\text{Ni} \): Number of neutrons = 61 - 28
- \( ^{62}\text{Ni} \): Number of neutrons = 62 - 28
- \( ^{64}\text{Ni} \): Number of neutrons = 64 - 28

Let me calculate this.### b) The number of neutrons in each isotope of nickel is as follows:

- \( ^{58}\text{Ni} \) has **30** neutrons.
- \( ^{60}\text{Ni} \) has **32** neutrons.
- \( ^{61}\text{Ni} \) has **33** neutrons.
- \( ^{62}\text{Ni} \) has **34** neutrons.
- \( ^{64}\text{Ni} \) has **36** neutrons.

Would you like further details or clarifications on any part?

Here are 5 related questions for further exploration:
1. How does the average atomic mass differ if another isotope is added?
2. How would the calculations change if the abundances were measured in different units?
3. Why do some elements have isotopes with very low abundances?
4. How is the atomic number determined for an element like nickel?
5. What is the significance of isotopes in chemical reactions?

**Tip**: Remember that the abundance of isotopes directly affects the average atomic mass of an element!

a) Calculate the average atomic mass of nickel. b) Determine the number of neutrons in each isotope of nickel.

This problem involves calculating the average atomic mass of nickel based on its isotopes and determining the number of neutrons in each isotope. It covers key concepts like weighted average and atomic structure, suitable for high school students.

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