Calculate the relative atomic mass of potassium given that it exists as K-39 and K-41 with natural abundances of 93.1% and 6.9% respectively.

Understand the Problem

The question is asking to calculate the relative atomic mass of potassium based on its natural abundances as well as the respective isotopic masses. This involves using the known isotopic mass of potassium isotopes and their abundance percentages.

Answer

The relative atomic mass of potassium is approximately $ 39.258 \, \text{amu} $.

Steps to Solve

Identify the isotopes and their abundances
- The isotopes of potassium we need to consider are K-39 and K-41.
- Their natural abundances are:
  - K-39: 93.1%
  - K-41: 6.9%
Convert percentages to fractions
- We will convert the percentages into fractions for calculation:
  - K-39: ( \frac{93.1}{100} = 0.931 )
  - K-41: ( \frac{6.9}{100} = 0.069 )
Multiply each isotope's mass by its corresponding abundance
- The isotopic masses are K-39 = 39 amu and K-41 = 41 amu.
- Calculate the contribution of each isotope:
  - For K-39: $$ 39 \times 0.931 = 36.429 \text{ amu} $$
  - For K-41: $$ 41 \times 0.069 = 2.829 \text{ amu} $$
Add the contributions from both isotopes
- Finally, add the contributions to find the relative atomic mass of potassium: $$ \text{Relative Atomic Mass} = 36.429 + 2.829 = 39.258 \text{ amu} $$

The relative atomic mass of potassium is approximately ( 39.258 , \text{amu} ).

More Information

The calculated relative atomic mass gives insight into the average mass of potassium atoms in natural samples, factoring in the distribution of its isotopes. Potassium has important biological roles, especially in neural function.

Tips

Forgetting to convert percentages to fractions: Make sure to always convert the natural abundances from percentages to decimals (e.g., ( 93.1% = 0.931 )).
Not including both isotopes: It's crucial to calculate contributions of all relevant isotopes.

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