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 element Rz, we use the formula:
[
\text{Average atomic mass} = (\text{fraction of isotope 1} \times \text{mass of isotope 1}) + (\text{fraction of isotope 2} \times \text{mass of isotope 2})
]
Step 1: Identify Given Data
- Isotope 1: (^{169}Rz) has a mass of 168.94 amu.
- Isotope 2: (^{171}Rz) has a mass of 170.98 amu.
- Natural abundance: Out of every 15 atoms, 11 are (^{169}Rz), and the remaining 4 are (^{171}Rz).
Step 2: Convert Natural Abundance into Fractions
[
\text{Fraction of } ^{169}Rz = \frac{11}{15} = 0.7333
]
[
\text{Fraction of } ^{171}Rz = \frac{4}{15} = 0.2667
]
Step 3: Apply the Formula
[
\text{Average atomic mass} = (0.7333 \times 168.94) + (0.2667 \times 170.98)
]
[
= 123.94 + 45.60
]
[
= 169.54 \text{ amu}
]
Step 4: Choose the Closest Answer
The closest option to 169.54 amu is 169.48 amu.
Final Answer: (A) 169.48 amu
Explanation
The atomic mass of an element is a weighted average of its isotope masses, based on their relative natural abundances. Since (^{169}Rz) is much more abundant than (^{171}Rz), the final atomic mass is closer to 168.94 amu than to 170.98 amu. This method ensures precise calculation by considering both isotope masses and their natural occurrences.
