Question

question 12 (2 points)
a sample of naturally occurring leungstine consists lg - 28 (amu = 27.9769), lg - 29 (amu = 28.9765)
and lg - 30 (amu = 29.9738). if the weighted atomic mass of leungstine is 28.0855 and the natural
abundance of lg - 29 is 4.67%, what is the natural abundance of lg - 28?
what is the natural abundance of lg - 30?

Explanation:

Step1: Let the abundance of Lg - 28 be \(x\)

Since the sum of abundances of all isotopes is \(100\%\), the abundance of Lg - 30 is \(100-(x + 4.67)\)

Step2: Use the formula for weighted - atomic mass

The formula for weighted - atomic mass \(M=\sum_{i}m_{i}a_{i}\), where \(m_{i}\) is the mass of isotope \(i\) and \(a_{i}\) is the abundance of isotope \(i\) (in decimal form).
We know that \(28.0855=27.9769\times\frac{x}{100}+28.9765\times\frac{4.67}{100}+29.9738\times\frac{100-(x + 4.67)}{100}\)

First, simplify the equation:

$$
LATEXBLOCK0
$$

Then find the abundance of Lg - 30: \(100-(92.03 + 4.67)=3.3\)

Answer:

The natural abundance of Lg - 28 is approximately \(92.03\%\) and the natural abundance of Lg - 30 is \(3.3\%\)