An unknown element, Z, has 3 isotopes: Z5, Z6 and Z8. Given that the atomic mass of Z is 7, and the relative abundance of Z5 is 20%, which of the following statements are correct? 1. Z5 and Z6 are present in the same abundance. 2. Z8 is the most abundant of the isotopes. 3. Z8 is more abundant than Z5 and Z6combined. A. 1 only B. 2 only C. 3 only D. 1 and 3 E. 1, 2 and 3
Question
An unknown element, Z, has 3 isotopes: Z5, Z6 and Z8. Given that the atomic mass of Z is 7, and the relative abundance of Z5 is 20%, which of the following statements are correct?
- Z5 and Z6 are present in the same abundance.
- Z8 is the most abundant of the isotopes.
- Z8 is more abundant than Z5 and Z6combined.
A. 1 only
B. 2 only
C. 3 only
D. 1 and 3
E. 1, 2 and 3
Solution
To answer this question, we need to understand that the atomic mass of an element is the weighted average of the masses of its isotopes, taking into account their relative abundances.
We know that the atomic mass of Z is 7 and the relative abundance of Z5 is 20%.
Let's denote the relative abundances of Z6 and Z8 as x and y respectively. Since the sum of the relative abundances of all isotopes must be 100%, we have:
20% + x + y = 100% => x + y = 80%
The atomic mass of Z is calculated as follows:
7 = 0.205 + x6 + y*8
We can see that for the atomic mass to be 7, the contribution from Z8 (y8) must be greater than the contribution from Z6 (x6). This means that Z8 must be more abundant than Z6.
However, we cannot determine from the given information whether Z8 is more abundant than Z5 and Z6 combined, or whether Z5 and Z6 are present in the same abundance.
Therefore, the correct answer is B. 2 only.
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