Calculate the atomic mass of potassium if the abundance atomic masses of the isotopes making up its naturally occurring samples are as given below. Potassium-39 Relative abundance: 93.12% Atomic mass: 38.964 amu Potassium-41 Relative abundance: 6.88% Atomic mass: 40.962 amu
The Correct Answer and Explanation is:
To calculate the atomic mass of potassium based on the given isotope abundances and atomic masses, we need to use the weighted average formula. The formula for the average atomic mass is:Average atomic mass=∑(Fraction of isotope×Atomic mass of isotope)\text{Average atomic mass} = \sum \left( \text{Fraction of isotope} \times \text{Atomic mass of isotope} \right)Average atomic mass=∑(Fraction of isotope×Atomic mass of isotope)
Step 1: Convert the percentage abundances into decimal form
- Potassium-39: 93.12% = 0.9312
- Potassium-41: 6.88% = 0.0688
Step 2: Multiply the abundance of each isotope by its atomic mass
- Potassium-39 contribution:
0.9312×38.964=36.3056 amu0.9312 \times 38.964 = 36.3056 \text{ amu}0.9312×38.964=36.3056 amu
- Potassium-41 contribution:
0.0688×40.962=2.8176 amu0.0688 \times 40.962 = 2.8176 \text{ amu}0.0688×40.962=2.8176 amu
Step 3: Add these contributions to get the average atomic mass
Average atomic mass of potassium=36.3056+2.8176=39.1232 amu\text{Average atomic mass of potassium} = 36.3056 + 2.8176 = 39.1232 \text{ amu}Average atomic mass of potassium=36.3056+2.8176=39.1232 amu
Thus, the atomic mass of potassium is approximately 39.12 amu.
Explanation:
The atomic mass is essentially the weighted average of the atomic masses of all naturally occurring isotopes of an element. Since the isotopes have different abundances in nature, each isotope contributes to the overall atomic mass according to its relative abundance. In this case, potassium-39 contributes more to the atomic mass than potassium-41 because it has a higher abundance (93.12% compared to 6.88%).
By performing this weighted average calculation, we find that the atomic mass of potassium is approximately 39.12 amu, which is close to the commonly accepted atomic mass of potassium (39.10 amu). This reflects the fact that potassium-39 is the most abundant isotope.
