An unknown element Q has two known isotopes: 60Q and 63Q. If the average atomic mass is 62.0 amu, what are the relative percentages of the isotopes?

To determine the relative percentages of the isotopes, we need to use the average atomic mass and the known masses of the isotopes.

Let x be the percentage of the 60Q isotope, and (100 - x) be the percentage of the 63Q isotope. Since the atomic mass of an isotope is the product of its abundance (as a decimal) and its mass, we can set up the following equation:

(x/100) * 60 + ((100 - x)/100) * 63 = 62.0

Simplifying the equation:

(60x + 6300 - 63x)/100 = 62.0

(6300 - 3x)/100 = 62.0

Cross-multiply:

6300 - 3x = 6200

-3x = -100

x = 100/3 ≈ 33.33

Therefore, the percentage of the 60Q isotope is approximately 33.33%, and the percentage of the 63Q isotope is approximately 66.67%.

To find the relative percentages of the isotopes, we need to use the average atomic mass and the known isotopes.

Let's assume the relative percentage of the first isotope (60Q) is x.
So, the relative percentage of the second isotope (63Q) would be 1 - x.

To calculate the average atomic mass, we can use the formula:

Average Atomic Mass = (Relative Percentage of Isotope 1 * Mass of Isotope 1) + (Relative Percentage of Isotope 2 * Mass of Isotope 2)

Substituting the values, we get:

62.0 amu = (x * 60) + ((1 - x) * 63)

Now, let's solve this equation to find the value of x:

62.0 = 60x + 63 - 63x
62.0 - 63 = -3x
-1.0 = -3x
x = -1.0 / -3
x = 1/3

Therefore, the relative percentage of the first isotope (60Q) is 1/3, and the relative percentage of the second isotope (63Q) is 1 - 1/3 = 2/3.

To convert these fractions to percentages, we multiply by 100:

Relative percentage of 60Q = (1/3) * 100 = 33.33%
Relative percentage of 63Q = (2/3) * 100 = 66.67%

Hence, the relative percentages of the isotopes are approximately 33.33% for 60Q and 66.67% for 63Q.