Question

a. How many naturally occurring isotopes does magnesium have?

b. What is the weighted-average atomic mass of Magnesium in a sample that has the following isotopic abundance: 80%, 90%,99% (calculate based on the smallest to greatest values of the masses of the isotopes with the percent order, respectively)?

Answer 1

Please find attached the solution to the above question.

Answer 2

a. Naturally Occurring Isotopes of Magnesium

Magnesium has 3 naturally occurring isotopes:

• ²⁴Mg (abundance ~79%),

• ²⁵Mg (abundance ~10%),

• ²⁶Mg (abundance ~11%).

Answer: $\boxed{{\displaystyle 3}}$

---

b. Weighted-Average Atomic Mass of Magnesium

Given:

• Isotopic abundances: 80%, 90%, 99% (ordered from smallest to greatest isotope mass).

• Assume isotope masses (in atomic mass units, u) follow natural order:

• Lightest isotope ($m_1$) = 24 u (²⁴Mg),

• Middle isotope ($m_2$) = 25 u (²⁵Mg),

• Heaviest isotope ($m_3$) = 26 u (²⁶Mg).

Calculation:

1. Normalize abundances (must sum to 100%):
   Given percentages are 80%, 90%, 99% → Total = $80+90+99=269\mathrm{\%}$.
   Normalized abundances:

   $${\text{Abundance}}_1=\frac{80}{269}\approx 29.74\mathrm{\%},{\text{Abundance}}_2=\frac{90}{269}\approx 33.46\mathrm{\%},{\text{Abundance}}_3=\frac{99}{269}\approx 36.80\mathrm{\%}\mathrm{.}$$

2. Weighted-average atomic mass:

   $$\text{Average mass}=(0.2974\times 24)+(0.3346\times 25)+(0.3680\times 26)\mathrm{.}$$$$=7.1376+8.365+9.568=25.0706\text{u}\mathrm{.}$$

Answer: $\boxed{{\displaystyle 25.07\text{u}}}$ (rounded to 2 decimal places).