Math Snap

STEP 1

Assumptions1. The data table provides the natural abundance of three isotopes of an unknown element X Unknown-20, Unknown-21, and Unknown-22.
. The natural abundance is not yet expressed as a percentage.
3. The numbers20,21, and22 represent the mass numbers of the isotopes.

STEP 2

First, we need to calculate the total abundance of all isotopes. We can do this by adding the natural abundances of all isotopes.
$$Total\, abundance = Abundance_{20} + Abundance_{21} + Abundance_{22}$$

STEP 3

Now, plug in the given values for the natural abundances to calculate the total abundance.
$$Total\, abundance =9048 +27 +925$$

STEP 4

Calculate the total abundance.
$$Total\, abundance =9048 +27 +925 =10000$$

STEP 5

Now, we can calculate the relative abundance of each isotope as a percentage. The relative abundance of an isotope is the natural abundance of that isotope divided by the total abundance, multiplied by100%.
$$Relative\, abundance_{20} = \frac{Abundance_{20}}{Total\, abundance} \times100\%$$$$Relative\, abundance_{21} = \frac{Abundance_{21}}{Total\, abundance} \times100\%$$$$Relative\, abundance_{22} = \frac{Abundance_{22}}{Total\, abundance} \times100\%$$

STEP 6

Plug in the values for the natural abundances and the total abundance to calculate the relative abundances.
$$Relative\, abundance_{20} = \frac{9048}{10000} \times100\%$$$$Relative\, abundance_{21} = \frac{27}{10000} \times100\%$$$$Relative\, abundance_{22} = \frac{925}{10000} \times100\%$$

STEP 7

Calculate the relative abundances.
$$Relative\, abundance_{20} =90.48\%$$$$Relative\, abundance_{21} =0.27\%$$$$Relative\, abundance_{22} =9.25\%$$

STEP 8

The average atomic mass of an element is the sum of the products of the mass number and relative abundance of each isotope.$$Average\, atomic\, mass = Mass_{20} \times Relative\, abundance_{20} + Mass_{21} \times Relative\, abundance_{21} + Mass_{22} \times Relative\, abundance_{22}$$

STEP 9

Plug in the values for the mass numbers and the relative abundances to calculate the average atomic mass.
$$Average\, atomic\, mass =20 \times90.48\% +21 \times.27\% +22 \times9.25\%$$

Calculate the average atomic mass.
$$Average\, atomic\, mass =20 \times90.48\% +21 \times0.27\% +22 \times9.25\% =20.18$$The average atomic mass of the element is20.18. Looking at the periodic table, the element with an atomic mass closest to this is calcium (Ca), with an atomic mass of20.18. Therefore, the unknown element is likely to be calcium.
As for the mass spectrometer graph, it would have three peaks at mass numbers20,21, and22. The peak at20 would be the highest, representing the most abundant isotope, while the peak at21 would be the smallest, representing the least abundant isotope.