Iridium has only two naturally occurring isotopes. The mass of iridium-191 is 190.9605 amu and the mass of iridium-193 is 192.9629 amu . Use the atomic mass of iridium to calculate the relative abundance of iridium-193.

The percentage abundance of iridium-191 is 37% while the  percentage abundance of iridium-193 is 63%.

The relative atomic mass is defined as the sum of the masses of all the isotopes that compose an element. In this case, the following information are provided in the question;

Relative atomic mass of iridium = 192.217

Mass of  iridium-191 = 190.9605

Mass of iridium-193 = 192.9629

So, we have;

192.217 = 190.9605x +  192.9629(1 - x)

192.217 =  190.9605x +192.9629 - 192.9629x

192.217 - 192.9629 = 190.9605x -  192.9629x

-0.7459 = -2.0024x

x = 0.7459/2.0024

x = 0.37 or 37 %

Hence;

Percentage abundance of  iridium-191 = 37 %

Percentage abundance of iridium-193 = 100 - 37 = 63%

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Abundance of Iridium-193 is 62.75%

Explanation:

From the question given above, the following data were obtained:

Isotope A (Iridium-191):

Mass of A = 190.9605 amu

Abundance of A = A%

Isotope B (Iridium-193):

Mass of B = 192.9629 amu

Abundance B = (100 – A) %

Relative atomic mass of Iridium = 192.217 amu

Next, we shall determine the abundance of isotope A (Iridium-191). This can be obtained as follow:

Relative atomic mass = [(Mass of A × A%)/100] + [(Mass of B × B%)/100]

192.217 = [(190.9605 × A%)/100] + [(192.9629 × (100 – A)%)/100]

192.217 = 1.909605A% + 1.929629(100 – A)%

192.217 = 1.909605A% + 192.9629 – 1.929629A%

Collect like terms

192.217 – 192.9629 = 1.909605A% – 1.929629A%

–0.7459 = –0.020024A%

Divide both side by –0.020024

A% = –0.7459 / –0.020024

A% = 37.25 %

Finally, we shall determine the abundance of Isotope B (Iridium-193).

This can be obtained as follow:

Abundance of A (Iridium-191) = 37.25 %

Abundance of B (Iridium-193) =?

Abundance B = 100 – A%

Abundance B = 100 – 37.25 %

Abundance of B (Iridium-193) = 62.75%