Magnesium has an average atomic mass of 24.3068 amu and has three isotopes: 24Mg(23.985045 amu), 25 Mg (24.985839 amu) and 26 Mg(25.982595 amu) The 26 Mg isotope has an abundance of 11.1%. what are the abundances of the other two isotopes. Please show work
isotope 26 = 0.111
isotope 25 = x
isotope 24 = 1-x-0.111
(mass*fraction) + (mass*fraction) + (mass*fraction) = 24.3068
Solve for x.
To find the abundances of the other two isotopes of magnesium, we can use the information given.
Let's denote the abundance of 24Mg (A = 23.985045 amu) as x and the abundance of 25Mg (A = 24.985839 amu) as y.
Since the sum of all the isotopes' abundances should equal 100%, we can set up an equation:
x + y + 11.1% = 100%
First, let's convert the percentage to a decimal by dividing it by 100:
x + y + 0.111 = 1
Now we have one equation, but we need another equation to solve for two unknowns. The last piece of information we have is the average atomic mass of magnesium, which is calculated by weighting the atomic masses of each isotope by their respective abundances:
(0.111 * 25.982595 amu) + (x * 23.985045 amu) + (y * 24.985839 amu) = 24.3068 amu
Now we have two equations that we can solve simultaneously to find the values of x and y:
x + y + 0.111 = 1 (Equation 1)
(0.111 * 25.982595) + (x * 23.985045) + (y * 24.985839) = 24.3068 (Equation 2)
We can rearrange Equation 1 to solve for x:
x = 1 - y - 0.111
Substituting this into Equation 2:
(0.111 * 25.982595) + ((1 - y - 0.111) * 23.985045) + (y * 24.985839) = 24.3068
Now we can solve this equation for y by simplifying and solving for y.