What is the atomic mass of B if 19.9% of all B atoms have a mass of 10.01 amu and 80.1% have a mass of 11.01 amu?
A) 10.21 amu
B) 10.50 amu
C) 10.63 amu
D) 10.81 amu
The correct answer and explanation is :
To find the atomic mass of Boron (B), we need to calculate the weighted average of the isotopes based on their abundances and individual masses.
Given:
- 19.9% of Boron atoms have a mass of 10.01 amu.
- 80.1% of Boron atoms have a mass of 11.01 amu.
The formula to calculate the atomic mass (weighted average) is:
[
\text{Atomic mass} = (f_1 \times m_1) + (f_2 \times m_2)
]
Where:
- ( f_1 ) and ( f_2 ) are the fractional abundances of the two isotopes.
- ( m_1 ) and ( m_2 ) are the atomic masses of the isotopes.
Step 1: Convert percentages to fractions
- 19.9% = 0.199
- 80.1% = 0.801
Step 2: Apply the formula
[
\text{Atomic mass} = (0.199 \times 10.01 \, \text{amu}) + (0.801 \times 11.01 \, \text{amu})
]
Step 3: Calculate each term
[
0.199 \times 10.01 = 1.990
]
[
0.801 \times 11.01 = 8.812
]
Step 4: Add the terms
[
\text{Atomic mass} = 1.990 + 8.812 = 10.802 \, \text{amu}
]
Thus, the atomic mass of Boron is approximately 10.81 amu.
Conclusion:
The correct answer is D) 10.81 amu.
Explanation:
The atomic mass is the weighted average mass of an element’s naturally occurring isotopes. Each isotope’s contribution is weighted by its abundance in nature. In this case, Boron has two isotopes: one with a mass of 10.01 amu and the other with a mass of 11.01 amu. By considering their respective abundances (19.9% and 80.1%), we calculated the average atomic mass. The higher abundance of the 11.01 amu isotope pulls the average toward that value, resulting in an atomic mass of approximately 10.81 amu for Boron. This weighted average is crucial in understanding the behavior of elements in various chemical reactions and calculations.
