Question

part 2
consider the data below:

isotopes with a known natural abundance
mass number natural abundance half - life
24 78.99% stable
25 10.00% stable
26 11.01% stable

1. describe in detail the structure of these three isotopes. in what ways are they similar to and different from each other?
2. show a calculation for the average atomic mass. explain the reasoning behind your calculation. what units should it have? what element is this?
3. what is the neutron:proton ratio for the lightest isotope?
4. give an example of an extensive, quantitative, and physical property. can it be used to identify a substance? why or why not?

Explanation:

Step1: Structure of isotopes

Isotopes have same number of protons (same element) but different number of neutrons. For these isotopes, they all have the same number of protons which determines they are the same element. The difference lies in the number of neutrons, which gives them different mass - numbers.

Step2: Calculate average atomic mass

The formula for average atomic mass ($A_{avg}$) is $A_{avg}=\sum_{i} (A_i\times \%_i)$, where $A_i$ is the mass - number of the isotope and $\%_i$ is its natural abundance as a decimal.
For the given isotopes:

$$
LATEXBLOCK0
$$

The reasoning is that we are taking a weighted - average of the mass - numbers based on their natural abundances. The units are atomic mass units (amu). Looking at the periodic table, the element with an average atomic mass close to 24.3202 is magnesium (Mg).

Step3: Neutron - proton ratio for lightest isotope

The lightest isotope has a mass - number of 24. For magnesium, the atomic number (number of protons, $Z$) is 12. The number of neutrons ($N$) for the 24 - mass number isotope is $N = 24−12=12$. The neutron - proton ratio is $\frac{N}{Z}=\frac{12}{12}=1$.

Step4: Example of property

An example of an extensive, quantitative, and physical property is mass. Mass is extensive (depends on the amount of substance), quantitative (can be measured numerically), and physical (no chemical change occurs). It cannot be used to identify a substance uniquely because different substances can have the same mass. For example, 10 grams of iron and 10 grams of copper have the same mass but are different substances.

Answer:

1. They have the same number of protons (same element) and different number of neutrons.
2. Average atomic mass calculation: $A_{avg}=(24\times0.7899)+(25\times0.1000)+(26\times0.1101)=24.3202$ amu. Reasoning: weighted - average based on natural abundances. Element is magnesium (Mg).
3. 1
4. Mass is an example. It cannot be used to identify a substance uniquely as different substances can have the same mass.