There are two stable isotopes of Gallium Their masses are 68.92558 and 70.9247050 AMU. If the average atomic mass of gallium is 69.7231, what is the natural abundance of the lighter isotope?
I don't know where to start!
Let x = fraction of the lighter isotope.
1-x = fraction of the other isotope.
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x(lighter AMU) + (1-x)(other isotope)=avg.
Substitute and solve for x.
To determine the natural abundance of the lighter isotope of Gallium, you can set up an equation using the given average atomic mass and the masses of the two isotopes.
Let's represent the natural abundance of the lighter isotope as "x" (in decimal form).
The equation can be written as:
(68.92558 * x) + (70.9247050 * (1 - x)) = 69.7231
In this equation, the first term represents the contribution of the lighter isotope to the average atomic mass, and the second term represents the contribution of the heavier isotope.
Now, you can solve this equation to find the value of "x," which represents the natural abundance of the lighter isotope.
To find the natural abundance of the lighter isotope of gallium, we need to use the average atomic mass and the masses of the isotopes. Here's how you can calculate it:
Step 1: Assign variables:
Let's call the natural abundance of the lighter isotope x.
Step 2: Define the equation:
To find the average atomic mass, we use the formula:
Average atomic mass = (Mass of isotope 1 * Abundance of isotope 1) + (Mass of isotope 2 * Abundance of isotope 2)
In this case, the equation would be:
69.7231 AMU = (68.92558 AMU * x) + (70.9247050 AMU * (1 - x))
Step 3: Solve the equation:
Solve the equation to find the value of x (the natural abundance of the lighter isotope).
68.92558x + 70.9247050(1 - x) = 69.7231
Step 4: Simplify and solve for x:
Multiply the terms inside the parentheses:
68.92558x + 70.9247050 - 70.9247050x = 69.7231
Combine like terms:
-1.9991250x = -1.2016050
Divide by -1.9991250 to isolate x:
x ≈ -1.2016050 / -1.9991250
x ≈ 0.601
Step 5: Convert x to a percentage:
Multiply by 100 to convert the natural abundance to a percentage:
x ≈ 0.601 * 100 ≈ 60.1%
Therefore, the natural abundance of the lighter isotope of gallium is approximately 60.1%.