Silver (ag) has two stable isotopes: 107ag, 106.90 amu, and 109ag, 108.90 amu. if the average atomic mass of silver is 107.87 amu,
what is the natural abundance of each isotope? (expressed as a percentage)

Explanation:

The average atomic mass of silver can be expressed as:

107.87 = 106.90 * A1 + 108.90 * A2

Where A1 is the abundance of 107Ag and A2 of 109Ag.

Assuming those two isotopes are the only one stables, we can use the equation:

A1 + A2 = 1.0

So now we have a system of two equations with two unknowns, and what's left is algebra.

First we use the second equation to express A1 in terms of A2:

A1 = 1.0 - A2

We replace A1 in the first equation:

107.87 = 106.90 * A1 + 108.90 * A2

107.87 = 106.90 * (1.0-A2) + 108.90 * A2

107.87 = 106.90 - 106.90*A2 + 108.90*A2

107.87 = 106.90 + 2*A2

2*A2 = 0.97

A2 = 0.485

So the abundance of 109Ag is (0.485*100%) 48.5%.

We use the value of A2 to calculate A1 in the second equation:

A1 + A2 = 1.0

A1 + 0.485 = 1.0

A1 = 0.515

So the abundance of 107Ag is 51.5%.

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.

2b2t

explanation:

2b2t