Final answer:
The percentage of the indium-115 isotope in a mixture that has an average atomic mass of 114.8 amu can be calculated using the equation for average atomic mass. After setting up the equation with the mass numbers of In-113 and In-115 and solving for the abundance of In-113, we find that the In-115 isotope makes up 90% of the mixture.
Step-by-step explanation:
To calculate the percentage of the isotope indium-115 in a mixture of In-113 and In-115, given an average atomic mass of 114.8 amu, We can use the concept of average atomic mass which is calculated based on the abundance of isotopes.
Let's represent the fraction of In-113 in the mixture as x, and therefore the fraction of In-115 would be 1-x (since the total must equal 1). Since In-113 has a mass number of 113 and In-115 has a mass number of 115, we can set up the equation for the average atomic mass:
114.8 = (x × 113) + ((1-x) × 115)
Solving for x, we can determine the abundance of In-113. Once we know the value of x, we can easily calculate the percentage of In-115 by doing (1-x) × 100%.
Substituting the known values into the equation, we get:
114.8 = (x × 113) + ((1-x) × 115)
114.8 = 113x + 115 - 115x
114.8 = 115 - 2x
2x = 115 - 114.8
2x = 0.2
x = 0.1
To find the abundance of In-115, calculate (1-x):
1 - 0.1 = 0.9
The percentage of In-115 in the mixture is therefore 90%.