Answer:
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%
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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