Copper has two naturally occurring isotopes with atomic masses of 62.9296 u () and 64.9278 u (). The atomic mass of copper is 63.546 u. What is the percent distribution of the isotopes

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Question:

Copper has two naturally occurring isotopes with atomic masses of 62.9296 u () and 64.9278 u (). The atomic mass of copper is 63.546 u. What is the percent distribution of the isotopes

Answer:

Answer:

The abundance of first isotope is 69.15 %

The abundance of second isotope is 30.85 %

Explanation:

The formula for the calculation of the average atomic mass is:

?f=Average%5C%20atomic%5C%20mass%3D(%5Cfrac%20%7B%5C%25%5C%20of%5C%20the%5C%20first%5C%20isotope%7D%7B100%7D%5Ctimes%20%7BMass%5C%20of%5C%20the%5C%20first%5C%20isotope%7D)%2B(%5Cfrac%20%7B%5C%25%5C%20of%5C%20the%5C%20second%5C%20isotope%7D%7B100%7D%5Ctimes%20%7BMass%5C%20of%5C%20the%5C%20second%5C%20isotope%7D)

Given that:

Since the element has only 2 isotopes, so the let the percentage of first be x and the second is 100 -x.

For first isotope:

% = x %

Mass = 62.9296 u

For second isotope:

% = 100  – x  

Mass = 64.9278 u

Given, Average Mass = 63.546 u

Thus,  

?f=63.546%3D%5Cfrac%7Bx%7D%7B100%7D%5Ctimes%20%7B62.9296%7D%2B%5Cfrac%7B100

Solving for x, we get that:

x = 69.15 %

The abundance of first isotope is 69.15 %

The abundance of second isotope is 100 – 69.15 % = 30.85 %

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