An unknown element Q has two known isotopes: 60Q and 63Q. If the average atomic mass is 60.5 amu, what are the relative percentages of the isotopes?
To find the relative percentages of the isotopes, we can use the concept of average atomic mass. The average atomic mass is the weighted average of the masses of all the isotopes of an element, taking into account their relative abundance.
Let's assume the relative percentage of the isotope 60Q is x%, and the relative percentage of the isotope 63Q is (100 - x)%.
The average atomic mass is calculated using the following formula:
Average atomic mass = (Percentage of isotope 1 * Mass of isotope 1 + Percentage of isotope 2 * Mass of isotope 2) / 100
Given that the average atomic mass is 60.5 amu, the mass of isotope 60Q is 60 amu, and the mass of isotope 63Q is 63 amu, we can substitute these values into the formula:
60.5 amu = (x/100 * 60 amu) + ((100 - x)/100 * 63 amu)
Let's solve this equation to find the value of x:
60.5 amu = 0.6x amu + 0.63(100 - x) amu
60.5 amu = 0.6x amu + 63 amu - 0.63x amu
60.5 amu - 63 amu = -0.03x amu
-2.5 amu = -0.03x amu
x = (-2.5 amu) / (-0.03 amu)
x ≈ 83.33
The relative percentage of the isotope 60Q is approximately 83.33%, and the relative percentage of the isotope 63Q is approximately (100 - 83.33)%, which is approximately 16.67%.
To find the relative percentages of the isotopes, we can use the concept of weighted average.
Let's assume the relative percentage of 60Q is x%, and the relative percentage of 63Q is (100-x)%. The average atomic mass of 60Q and 63Q is given as 60.5 amu.
To calculate the weighted average, we use the following formula:
(Percentage of first isotope * mass of first isotope) + (Percentage of second isotope * mass of second isotope) = Average atomic mass
(x/100 * 60u) + ((100-x)/100 * 63u) = 60.5u
Simplifying the equation, we get:
(60x + 6300 - 63x) / 100 = 60.5
(-3x + 6300) / 100 = 60.5
-3x + 6300 = 6050
-3x = -250
x = -250 / -3
x = 83.33
Therefore, the relative percentage of 60Q is approximately 83.33%, and the relative percentage of 63Q is approximately (100 - 83.33) = 16.67%.