An unknown element Q has two known isotopes: 61Q and 62Q. If the average atomic mass is 61.4 amu, what are the relative percentages of the isotopes?
Let x = fraction of 61Q
Then 1-x = fraction of 62Q
=============================
x*61 + (1-x)*62 = 61.4
Solve for x and 1-x, then convert to percent.
To calculate the relative percentages of isotopes, we need to understand the relationship between the mass of each isotope and its abundance.
Let's assume that x represents the relative abundance of the 61Q isotope and (1-x) represents the relative abundance of the 62Q isotope.
To find the average atomic mass (A_avg), we can use the formula:
A_avg = (mass_1 x abundance_1) + (mass_2 x abundance_2)
Given that the average atomic mass is 61.4 amu and the known masses of the isotopes are 61 amu and 62 amu, we can set up the equation:
61.4 = (61 x x) + (62 x (1-x))
Now, we can solve this equation to find the value of x, which represents the relative abundance of the 61Q isotope:
61.4 = 61x + 62 - 62x
61.4 - 62 = -x + x
-0.6 = -x
x = 0.6
Therefore, the relative abundance of the 61Q isotope is 0.6, and the relative abundance of the 62Q isotope is (1-0.6) = 0.4.
To express these values as percentages:
Percentage of 61Q isotope = (0.6) x 100% = 60%
Percentage of 62Q isotope = (0.4) x 100% = 40%
So, the relative percentages of the isotopes 61Q and 62Q are 60% and 40%, respectively.