Copper has 2 known isotopes: ^63CU atomic mass= 62.9298 and ^65 CU atomic mass=64.9278. The average atomic mass of copper is 63.546 amu. Calculate the fraction(percent) of each of the 2 isotopes of copper
63.546=X*62.9298+ (1-X)64.9278
where X is the decimal precent of Cu63, and 1-x is the decimal percent of Cu65
I am not understand
To calculate the fraction (percent) of each isotope of copper, we need to use the concept of weighted average. The atomic mass of an element is the weighted average of the masses of its isotopes, where the weights are the relative abundance of each isotope.
Let's assume the fraction (percent) of ^63CU is x and the fraction (percent) of ^65CU is y.
We can set up the following equations:
x + y = 100 (since the fractions should add up to 100%)
And,
(x/100) * 62.9298 + (y/100) * 64.9278 = 63.546
Simplifying the second equation, we get:
0.629298x + 0.649278y = 63.546
Now we can solve these two equations simultaneously to find the values of x and y.
One way to solve these equations is by substitution. Rearrange the first equation to express x in terms of y:
x = 100 - y
Substitute this expression for x in the second equation:
0.629298(100 - y) + 0.649278y = 63.546
Simplify and solve for y:
62.9298 - 0.629298y + 0.649278y = 63.546
0.01998y = 0.6162
y ≈ 30.82
Now substitute the value of y into the first equation to find x:
x + 30.82 = 100
x ≈ 69.18
Therefore, the fraction (percent) of ^63CU is approximately 69.18% and the fraction (percent) of ^65CU is approximately 30.82%.