To find the percentage of each isotope, we can use the concept of weighted average.
Let's assume x represents the percentage of 17Cl35 and y represents the percentage of 17Cl37.
Given that the average atomic mass of chlorine (Cl) is 35.5u, we can set up the following equation:
(17Cl35 * x) + (17Cl37 * y) = 35.5
We also know that the sum of the percentages of both isotopes should equal 100%, so we have the second equation:
x + y = 100
To solve these equations, we can use the method of substitution.
Rearranging the second equation, we have:
y = 100 - x
Substituting this value into the first equation:
(17Cl35 * x) + (17Cl37 * (100 - x)) = 35.5
Expanding and simplifying the equation:
17Cl35x + 17Cl37(100 - x) = 35.5
17Cl35x + 1700Cl37 - 17Cl37x = 35.5
(17Cl35 - 17Cl37)x + 1700Cl37 = 35.5
(17Cl35 - 17Cl37)x = 35.5 - 1700Cl37
x = (35.5 - 1700Cl37) / (17Cl35 - 17Cl37)
Now, let's substitute the atomic masses of the isotopes:
x = (35.5 - 1700(37)) / (35 - 37) x = (35.5 - 62900) / (-2) x = (-62564.5) / (-2) x = 31282.25
Since x represents the percentage of 17Cl35, and we know that the sum of the percentages should be 100%, we can find y:
y = 100 - x y = 100 - 31282.25 y = 68717.75
Therefore, the percentage of 17Cl35 is approximately 31.28%, and the percentage of 17Cl37 is approximately 68.72%.