Acarbonatomhasarelativeatomicmassof13.4.60%ofthecarbonatomhasamassnumberof12.8.30%ofthecarbonatomshaveamassnumberof13.5,whilsttheremaining10%haveamassnumberwhichisnotknown.Calculatethemassnumberofthecarbonisotopewhichis10%oftheCarbon13.4atom.Giveyouranswerto1decimalplace,ifneeded.
Question
Acarbonatomhasarelativeatomicmassof13.4.60%ofthecarbonatomhasamassnumberof12.8.30%ofthecarbonatomshaveamassnumberof13.5,whilsttheremaining10%haveamassnumberwhichisnotknown.Calculatethemassnumberofthecarbonisotopewhichis10%oftheCarbon13.4atom.Giveyouranswerto1decimalplace,ifneeded.
Solution
The question is asking for the mass number of the carbon isotope that makes up 10% of the Carbon 13.4 atom.
First, let's break down the information given:
- 60% of the carbon atom has a mass number of 12.8
- 30% of the carbon atom has a mass number of 13.5
- 10% of the carbon atom has an unknown mass number
The relative atomic mass of an element is calculated by taking the weighted average of the atomic masses of its isotopes. The formula for this is:
Relative atomic mass = (fraction of isotope 1 x mass of isotope 1) + (fraction of isotope 2 x mass of isotope 2) + ... + (fraction of isotope n x mass of isotope n)
We know the relative atomic mass of the carbon atom is 13.4, so we can set up the following equation:
13.4 = (0.60 x 12.8) + (0.30 x 13.5) + (0.10 x unknown mass)
Solving for the unknown mass, we get:
Unknown mass = (13.4 - (0.60 x 12.8) - (0.30 x 13.5)) / 0.10
Calculating the values, we get:
Unknown mass = (13.4 - 7.68 - 4.05) / 0.10
Unknown mass = 1.67 / 0.10
Unknown mass = 16.7
So, the mass number of the carbon isotope that makes up 10% of the Carbon 13.4 atom is 16.7.
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