An element with relative atomic mass 20.8 is found to contain 2 isotopes having a relative atomic mass of 20 and 21.Find the % composition of the element.
Relative atomic mass = 20.8 g
Let the fraction that is element 20 = x
thus the fraction that is element 21=1-x
so 20x +21(1-x) = 20.8
20x + 21 -21x=20.8
-1x=-0.2
x=0.2 and 1-x=0.8
so 20% element 20 and 80% element 21.
20.8%
To find the percentage composition of the element, we need to determine the relative abundance of each isotope. Let's denote the abundance of the isotope with a mass of 20 as x and the abundance of the isotope with a mass of 21 as y.
Since the atomic masses of the isotopes are given as 20 and 21, respectively, we can set up the following equation:
(20 * x) + (21 * y) = 20.8
We also know that the sum of the abundances is equal to 1, so we have another equation:
x + y = 1
Now we have a system of two equations:
(20 * x) + (21 * y) = 20.8
x + y = 1
To solve this system, we can use either substitution or elimination method. Let's use the substitution method.
Rearrange the second equation to get:
x = 1 - y
Substitute this value of x into the first equation:
(20 * (1 - y)) + (21 * y) = 20.8
Simplify and solve for y:
20 - 20y + 21y = 20.8
y = 0.8
Now substitute the value of y back into the second equation to find x:
x + 0.8 = 1
x = 0.2
Thus, the relative abundance of the isotope with a mass of 20 is 0.2 and the relative abundance of the isotope with a mass of 21 is 0.8.
To find the percentage composition of each isotope, we multiply the relative abundance (as a decimal) by 100:
Percentage composition of isotope with mass 20 = 0.2 * 100 = 20%
Percentage composition of isotope with mass 21 = 0.8 * 100 = 80%
Therefore, the element is composed of approximately 20% of the isotope with a mass of 20 and 80% of the isotope with a mass of 21.