A carbon atom has a relative atomic mass of 12.7.
75% of the carbon atom has a mass number of 12.9, whilst the remaining 25% has a mass number which is not known.
Calculate the mass number of the carbon isotope which is 25% of the Carbon 12.7 atom. Give your answer to 2 decimal places.
We can start by using the weighted average formula:
average atomic mass = (% abundance of isotope 1 x mass of isotope 1) + (% abundance of isotope 2 x mass of isotope 2)
We know that 75% of the carbon atom has a mass number of 12.9, so we can assign the following values:
% abundance of isotope 1 = 75%
mass of isotope 1 = 12.9
We also know that the remaining 25% of the atom has a mass number that is not known, so we can assign the following values:
% abundance of isotope 2 = 25%
mass of isotope 2 = x (unknown)
Plugging these values into the formula, we get:
12.7 = (0.75 x 12.9) + (0.25 x x)
Simplifying and solving for x, we get:
x = (12.7 - 0.75 x 12.9) / 0.25
x = 12.46
Therefore, the mass number of the carbon isotope which is 25% of the Carbon 12.7 atom is 12.46.
To calculate the mass number of the carbon isotope that is 25% of the Carbon 12.7 atom, we first need to determine the mass number of the known isotope (75% of the atom).
Given that 75% of the carbon atom has a mass number of 12.9, we can calculate its atomic mass using the formula:
Atomic mass = (% abundance × mass number) + (% abundance × mass number) + ...
Plugging in the values:
12.7 = (75% × 12.9) + (25% × mass number)
Now, let's solve for the unknown mass number:
12.7 = (0.75 × 12.9) + (0.25 × mass number)
12.7 = 9.675 + 0.25 × mass number
12.7 - 9.675 = 0.25 × mass number
2.025 = 0.25 × mass number
Dividing both sides by 0.25:
8.1 = mass number
Therefore, the mass number of the carbon isotope that is 25% of the Carbon 12.7 atom is 8.1.