Question

isotope abundance and atomic mass in nature, most elements occur as a mixture of two or more isotopes. each isotope of an element has a fixed mass and a natural percent abundance. comparing abundances of bromine, chlorine, and silicon isotopes bromine atomic mass = 79.904 amu chlorine atomic mass = 35.453 amu silicon atomic mass = 28.086 amu 15 sep analyze data look at the graphs. how does an elements atomic mass compare to the mass number of its most abundant isotope? the average atomic mass, or atomic mass for short, of an element is a weighted average of the masses of its isotopes. a weighted average mass reflects the masses and the relative abundances of the isotopes as they occur in nature. 16 sep use computational thinking copper has two isotopes, copper - 63 and copper - 65. it has an atomic mass of 63.546 amu. sketch a pie graph that shows the approximate abundance of each copper isotope based on the atomic mass.

Explanation:

Step1: Recall the concept of average atomic mass

The average atomic mass is a weighted - average of isotopic masses based on their natural abundances.

Step2: Analyze Bromine

For bromine, atomic mass is 79.904 amu. Bromine - 79 and bromine - 81 have nearly equal abundances. The average atomic mass is close to the average of 79 and 81.

Step3: Analyze Chlorine

Chlorine has an atomic mass of 35.453 amu. Chlorine - 35 is more abundant than chlorine - 37. The average atomic mass is closer to 35.

Step4: Analyze Silicon

Silicon has an atomic mass of 28.086 amu. Silicon - 28 is the most abundant isotope and the average atomic mass is close to 28.
In general, the atomic mass of an element is close to the mass number of its most abundant isotope because the most abundant isotope contributes the most to the weighted - average.

For the copper problem:
Let the abundance of copper - 63 be $x$, then the abundance of copper - 65 is $1 - x$.
The average atomic mass formula is $63x+65(1 - x)=63.546$.

Step1: Expand the equation

$63x + 65-65x=63.546$.

Step2: Combine like - terms

$- 2x=63.546 - 65=-1.454$.

Step3: Solve for $x$

$x=\frac{1.454}{2}=0.727$ or 72.7% (abundance of copper - 63), and $1 - x = 0.273$ or 27.3% (abundance of copper - 65).
To sketch the pie - graph, draw a circle. The sector for copper - 63 should take up approximately 72.7% of the circle's area and the sector for copper - 65 should take up approximately 27.3% of the circle's area.

Answer:

For the first part: The atomic mass of an element is close to the mass number of its most abundant isotope because the most abundant isotope contributes the most to the weighted - average of the isotopic masses.
For the second part: Copper - 63 has an approximate abundance of 72.7% and copper - 65 has an approximate abundance of 27.3% in the pie - graph.