A hypothetical element, Rz, has two isotopes: 169Rz = 168.94 amu and 171Rz = 170.98 amu. Eleven of every fifteen atoms of Rz found in nature exist as the 169Rz isotope. What is the average atomic mass of the element Rz?
A) 169.48 amu
B) 168.95 amu
C) 170.56 amu
D) 171.01 amu
The correct answer and explanation is :
To find the average atomic mass of the element Rz, we need to calculate the weighted average based on the isotopic masses and their relative abundances. Here’s how we can do that:
Given:
- Two isotopes of Rz:
- 169Rz has a mass of 168.94 amu.
- 171Rz has a mass of 170.98 amu.
- The abundance of 169Rz is 11 out of every 15 atoms.
- This means that the fraction of 169Rz in nature is ( \frac{11}{15} ).
- The remaining 4 out of every 15 atoms are 171Rz.
- This means the fraction of 171Rz in nature is ( \frac{4}{15} ).
Step-by-Step Calculation:
The average atomic mass of the element Rz is calculated using the formula:
[
\text{Average Atomic Mass} = ( \text{fraction of 169Rz} \times \text{mass of 169Rz}) + ( \text{fraction of 171Rz} \times \text{mass of 171Rz})
]
Substitute the values:
[
\text{Average Atomic Mass} = \left( \frac{11}{15} \times 168.94 \right) + \left( \frac{4}{15} \times 170.98 \right)
]
First, calculate each term:
- ( \frac{11}{15} \times 168.94 = 123.98 )
- ( \frac{4}{15} \times 170.98 = 45.59 )
Now, add them together:
[
123.98 + 45.59 = 169.57 \, \text{amu}
]
Conclusion:
The average atomic mass of Rz is approximately 169.57 amu, which is closest to option A) 169.48 amu.
