percent abundance of each isotope of Bromine

Question

If bromine has only two naturally occurring isotopes bromine-78 and bromine-81, calculate the percent abundance of each isotope.

(note: this is the only information provided in the problem. The atomic mass of each is not given. Would appreciate guidance on how to solve this)

Answer 1

I think you would assume the mass is 78 for Br-78 and 81 for Br-81.

You can set up a system of equations

Abundance for Br-78 is x, Abundance for Br-81 is y, where x and y are decimals.

x + y = 1

78x + 81y = 79.904

solve for x (or y)

x = 1-y

plug in x into second equation:

78(1-y) + 81y = 79.904

78 - 78y+81y = 78 + 3y = 79.904

solve for y:

y = 0.635

solve for x: from x = 1-y

x = 1-0.635 = 0.365

Abundance for Br-78 is x, Abundance for Br-81 is y, where x and y are decimals. Convert them to percentages.

Br-78 63.5%

Br-81 36.5%