What is the RAM of carbon in a sample based on data from a mass spectrum?

[123Sub-Zero]

1.Some data obtained from the mass spectrum of a sample of carbon are given below.
Ion 12C+ 13C+
Absolute mass of one ion/g 1.993 x 10-23 2.158 x 10-23
Relative abundance/ % 98.9 1.1
Use the data to calculate the mass of one neutron, the RAM of 13C and the RAM of carbon in the sample.
You may neglect the mass of an electron.
Work out:
1.Mass of one neutron
2.RAM of 13C
3.RAM of carbon in the sample
I know how to work out the RAM form a mass spectrometer graph but cannot work this out. I presume you multiply the mass of one ion by relative abundance to (for the RAM questions) but then don't know the next step.

 

[Mad_About_Science]

$$A_{r} of samples:\\ ^{13}C:~~\frac{13 x 1.1}{100} = 1.43 x 10^{-1} = 0.143\\ Carbon:~~\frac{(12 x 98.9)~+~(13 x 1.1)}{(98.9 + 1.1)} = 12.011 = 12$$

 

[Blueshift5]

In order to calculate the mass of one neutron, we can use the fact that the mass of one ion is equal to the mass of one proton plus the mass of one neutron. Therefore, we can subtract the mass of one proton (1.0073 amu) from the mass of 12C+ (1.993 x 10^-23 g) to get the mass of one neutron, which is approximately 1.986 x 10^-23 g.

To calculate the RAM of 13C, we can use the formula for calculating average atomic mass. This formula takes into account the mass and relative abundance of each isotope present. In this case, we have two isotopes, 12C and 13C, with relative abundances of 98.9% and 1.1%, respectively. Plugging these values into the formula, we get:

RAM = (98.9/100)(12 amu) + (1.1/100)(13 amu)
= 11.868 amu + 0.143 amu
= 12.011 amu

Therefore, the RAM of 13C is approximately 12.011 amu.

To calculate the RAM of carbon in the sample, we can use the same formula but with the relative abundance of 12C as 100%, since it is the only isotope present in carbon. This gives us:

RAM = (100/100)(12 amu)
= 12 amu

Therefore, the RAM of carbon in the sample is approximately 12 amu.