High School

Gold has two common isotopes, [tex]$Au-197$[/tex] and [tex]$Au-195$[/tex]. Based on the atomic mass on the periodic table, which should be more abundant?

A. [tex]$Au-197$[/tex]
B. [tex]$Au-195$[/tex]

Answer :

To determine which of the gold isotopes, [tex]\( Au-197 \)[/tex] or [tex]\( Au-195 \)[/tex], is more abundant, we need to compare their masses to the atomic mass of gold listed on the periodic table. The atomic mass of gold according to the periodic table is approximately [tex]\( 196.97 \)[/tex].

Here's how you can figure out which isotope is more abundant:

1. Determine the Mass of Each Isotope:
- [tex]\( Au-197 \)[/tex] has a mass number of 197.
- [tex]\( Au-195 \)[/tex] has a mass number of 195.

2. Compare Each Isotope's Mass to the Periodic Table Mass:
- Calculate the difference between the periodic table mass of gold ([tex]\( 196.97 \)[/tex]) and each isotope's mass.

3. Calculate the Difference:
- For [tex]\( Au-197 \)[/tex]:
[tex]\[
\text{Difference} = |196.97 - 197| = 0.03
\][/tex]
- For [tex]\( Au-195 \)[/tex]:
[tex]\[
\text{Difference} = |196.97 - 195| = 1.97
\][/tex]

4. Determine Which Isotope is More Abundant:
- The isotope with the smaller difference from the periodic table mass is more abundant because the periodic table mass is a weighted average that is closer to the mass of the more prevalent isotope.
- [tex]\( Au-197 \)[/tex] has a difference of 0.03, which is smaller than the difference for [tex]\( Au-195 \)[/tex], which is 1.97.

Therefore, [tex]\( Au-197 \)[/tex] is more abundant than [tex]\( Au-195 \)[/tex].

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