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Q.40

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

| The element gallium has two stable isotopes: 69 Ga with an atomic mass of 68.92 u and 71 Ga with an atomic mass of 70.92 u. A periodic table shows that the chemical atomic mass of gallium is 69.72 u. What is the percent abundance of 69 Ga?

Calculate the percent abundance of nucleus 69Ga.

Consider x1 and x2 are the fractions of nuclei 69Ga and 71Ga respectively. The total fraction of two isotopes is equal to one. That is,

x1+x2=1

Rearrange the equation for x2

x2 =1-x1

See the step by step solution

Step by Step Solution

The chemical atomic mass of gallium is equal to the x1 times of atomic mass of 69Ga plus x2times of atomic mass of 71Ga

That is,

Substitute 1-x2 for x2 in the above equation and solve for x1

Therefore, the abundance percentage of nucleus 69Ga is 60 %.

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