Question

1. the graph to the right shows part of the mass spectrum for a sample of an element. calculate the relative atomic mass. what is the identity of the element?
2. gallium has two naturally occurring isotopes, ga - 69 (68.93 amu) and ga - 71 (70.92 amu). if the average atomic mass of gallium is 69.72 amu, what is the percent abundance of each isotope?

Explanation:

14. Since the graph is not provided, we can't calculate the relative - atomic mass. But the general method to calculate the relative atomic mass from a mass - spectrum is as follows:

Step1: Identify isotopes and their abundances

Let the isotopes be \(I_1, I_2,\cdots, I_n\) with masses \(m_1, m_2,\cdots, m_n\) and relative abundances \(a_1\%, a_2\%,\cdots, a_n\%\) respectively.

Step2: Use the formula for relative atomic mass

The relative atomic mass \(A_r=\sum_{i = 1}^{n}m_i\times\frac{a_i}{100}\)

To identify the element, we compare the calculated relative atomic mass with the known relative atomic masses of elements in the periodic table.

15.

Step1: Let the percent abundance of Ga - 69 be \(x\), then the percent abundance of Ga - 71 is \((100 - x)\)

We know that the average atomic mass \(A_r\) is given by the formula \(A_r=m_1\times\frac{a_1}{100}+m_2\times\frac{a_2}{100}\)
Here, \(m_1 = 68.93\) amu, \(a_1=x\), \(m_2 = 70.92\) amu, \(a_2=(100 - x)\) and \(A_r = 69.72\) amu.
So, \(69.72=68.93\times\frac{x}{100}+70.92\times\frac{100 - x}{100}\)

Step2: Multiply through by 100 to clear the fractions

\(6972=68.93x+7092-70.92x\)

Step3: Combine like - terms

\(6972 - 7092=68.93x-70.92x\)
\(- 120=-1.99x\)

Step4: Solve for \(x\)

\(x=\frac{120}{1.99}\approx60.3\)
The percent abundance of Ga - 69 is approximately \(60.3\%\) and the percent abundance of Ga - 71 is \(100 - 60.3 = 39.7\%\)

Answer:

1. Insufficient data to calculate relative atomic mass and identify element.
2. Percent abundance of Ga - 69: \(60.3\%\), Percent abundance of Ga - 71: \(39.7\%\)