If an element N has isotopic abundances X% of mass number 12, atomic number 6, and Y% of N of mass number 13, atomic number 6. If their relative isotopic mass is 12.35. Find X and Y.
To find X and Y, we can set up two equations using the information given.
Let's assume that the mass of isotope N-12 is A and the mass of isotope N-13 is B.
We know that the isotopic abundances of N-12 and N-13 add up to 100%. Thus, the first equation we can write is:
X + Y = 100 (Equation 1)
The relative isotopic mass is given by:
(X * A) + (Y * B) = 12.35 (Equation 2)
Since we know the atomic numbers and mass numbers of both isotopes, we can find their respective atomic masses from the periodic table.
The atomic mass of carbon-12 (N-12) is exactly 12 units and the atomic mass of carbon-13 (N-13) is approximately 13.0034 units.
Let's substitute the atomic masses into Equation 2:
(X * 12) + (Y * 13.0034) = 12.35
Now, we have a system of two equations (Equation 1 and Equation 2) that we can solve to find the values of X and Y.
Using Equation 1, we can solve it for one variable and substitute into the other equation:
X = 100 - Y
Substituting X in Equation 2:
((100 - Y) * 12) + (Y * 13.0034) = 12.35
Expanding and simplifying:
1200 - 12Y + 13.0034Y = 12.35
1200 + 1.0034Y = 12.35
1.0034Y = 12.35 - 1200
1.0034Y = -1187.65
Y ≈ -1187.65 / 1.0034
Y ≈ -1182.71
Since the percentage values cannot be negative, we can conclude that there is an error or a typo in the given information or calculations. Please double-check the values provided and redo the calculations.