Abundance of isotopes based on ratios

[subopolois]

Homework Statement

how do i find abundances of isotopes of strontium if i am give their isotopic ratios and atomic masses

Homework Equations

The Attempt at a Solution

i know i have to find what the mass of each isotope is in the ratios to find the % abundance. i don't want to put up the actual numbers because i want to work this out myself. i just need a push in the right direction to get started

 

[chemisttree]

do the math on the ratios. they should sum to 1.

ie. 3:7 is 3/(3+7) or 0.3

 

[subopolois]

i should have mentioned that there are 4 isotopes, I am given 3 ratios and am told to find the abundance of each one
ie. 86Sr/88Sr= 0.12
84Sr/88Sr= 0.007
87Sr/86Sr= 2.5

i really don't know how to go about doing this

 

[symbolipoint]

The masses of the different isotopes can be assigned to variables, w, x, y, z for the Strontiums of masses 84, 86, 87, 88.

Those ratios you were given may then be stated as:
x/z = 0.12
w/z = 0.007
y/x = 2.5

All of the relative masses must sum to 1. This makes a necessary equation of this:
w + x + y + z = 1.0000

Now you have four equations using 4 unknown numbers. Those three ratio equations are convertible to linear equations, so the set of equations forms a fairly simple system of linear equations and should be fairly easily solvable.

 

[DeeNos]

To find the abundances of isotopes of strontium, you can use the following equation:

% abundance of isotope = (atomic mass of isotope / total atomic mass of all isotopes) * 100

To start, you need to determine the atomic mass of each isotope. This can be found by multiplying the mass of each isotope by its respective ratio. For example, if the ratio of strontium-86 is 0.82 and its atomic mass is 86, then the mass of strontium-86 would be 0.82 * 86 = 70.52.

Once you have the atomic masses of each isotope, you can then calculate the total atomic mass of all isotopes by adding them together. Then, plug these values into the equation above to find the % abundance of each isotope.

I hope this helps get you started in the right direction. Remember to double check your calculations and units to ensure accuracy. Good luck!