Bromine has two naturally occurring isotopes, the first of which is 79Br with a mass of 78.904 amu
and an abundance of 50.54%. Calculate the mass of the other isotope.
%abundance Br79 is 50.54%
Other isotope Br is 100-50.54 = 49.46%
(78.904*0.5054) + (mass*0.4946) = 79.904
Solve for mass (other isotope) = ?
To calculate the mass of the other isotope of bromine, let's denote it as xBr. We know that bromine has two isotopes, which means the sum of their abundances is equal to 100%.
The abundance of the first isotope is given as 50.54%. Therefore, the abundance of the second isotope can be expressed as (100% - 50.54%) = 49.46%.
Let's assume the mass of the second isotope (xBr) is x amu.
To calculate the average atomic mass of bromine, we can use the formula:
Average Atomic Mass = (Mass of Isotope 1 × Abundance of Isotope 1) + (Mass of Isotope 2 × Abundance of Isotope 2)
Using the given data, we have:
(78.904 amu × 50.54%) + (x amu × 49.46%) = Average Atomic Mass of Bromine
We can now solve the equation to find the value of x.
(78.904 × 0.5054) + (x × 0.4946) = Average Atomic Mass of Bromine
(39.8323816) + (0.4946x) = Average Atomic Mass of Bromine
0.4946x = Average Atomic Mass of Bromine - 39.8323816
Divide both sides by 0.4946 to isolate x:
x = (Average Atomic Mass of Bromine - 39.8323816) / 0.4946
Now, substitute the Average Atomic Mass of Bromine with its known value, 79.904 amu:
x = (79.904 amu - 39.8323816) / 0.4946
Evaluate the expression to get the mass of the other isotope:
x = 80.071 amu
Therefore, the mass of the other isotope of bromine is approximately 80.071 amu.