A newly discovered element, Mysternium (Atomic symbol My) has two isotopes and an average atomic mass of 296.7286 amu. One of the isotopes, My-296 has a natural abundance of 61.528% and has a mass value of 295.9064 amu. What is the mass of the second isotope?
The one isotope is 61.528%; the other one is 100-61.528.
(0.61528*295.9064)+ (0.38472*x) = 296.7286
Solve for x.
Thank you. I was so confused on what to do.
To find the mass of the second isotope, we need to subtract the mass of the first isotope from the average atomic mass and then divide it by the natural abundance of the second isotope.
Let's denote the mass of the second isotope as x.
We'll set up the following equation:
[x * (1 - 61.528%)] + [295.9064 amu * 61.528%] = 296.7286 amu.
First, we need to convert the natural abundance percentage to a decimal:
61.528% = 0.61528.
Now, we can rewrite the equation:
x * (1 - 0.61528) + 295.9064 amu * 0.61528 = 296.7286 amu.
Simplifying further:
0.38472x + 181.70461392 amu = 296.7286 amu.
Next, subtract 181.70461392 amu from both sides of the equation:
0.38472x = 296.7286 amu - 181.70461392 amu.
0.38472x = 115.02398608 amu.
Finally, divide both sides of the equation by 0.38472 to isolate x:
x = 115.02398608 amu / 0.38472.
x ≈ 299.020657 amu.
Therefore, the mass of the second isotope (My-299) is approximately 299.020657 amu.