Chlorine has two isotopes with mass number 35 and 37. Calculate the relative abundance of the two isotopes accounting for normal atomic mass of 35.5
35 x + 37(1-x) = 35.5
-2 x = -1.5
x = .75
1-x = .25
three times as much 35
YES
To calculate the relative abundance of the two isotopes of chlorine, we need to set up an equation using the average atomic mass of chlorine. Given that the average atomic mass of chlorine is 35.5, we can assign variables to represent the relative abundances of the isotopes.
Let x represent the relative abundance of the isotope with mass number 35, and y represent the relative abundance of the isotope with mass number 37. Since the sum of the relative abundances is equal to 1 (or 100%), we can express this relationship as follows:
x + y = 1
We can also use the atomic masses of each isotope to relate their abundances. The atomic mass of an isotope is calculated by multiplying the mass number by the relative abundance. For the isotope with mass number 35:
35 * x = ?
And for the isotope with mass number 37:
37 * y = ?
To solve for x and y, we need to set up another equation using the average atomic mass, which is given as 35.5. This can be expressed as:
(35 * x) + (37 * y) = 35.5
Now, we have a system of two equations with two variables:
x + y = 1
35x + 37y = 35.5
We can solve this system of equations to find the values of x and y, representing the relative abundances of the two isotopes of chlorine.