1. Let x = abundance of lighter isotopes (fraction)
QUESTION:
In a fictitious world, element Z has only two isotopes: 35Z with a mass of u and 37Z, with a mass of u. What is the relative abundance of the lighter isotope if the average mass is 35.8 u.
A %, B. 50.0%, C. 60.0%
Let x = abundance of lighter isotopes (fraction)
Z-35: mass=35.00 u, abundance = x
Z-37: mass=37.00 u, abundance = 1-x
35.80 u = (x)(35.00 u) + (1-x)(37.00 u)
35.80 = (x)(35.00) + (1-x)(37.00)
35.80 = 35.00x – 37.00x
35.80 = -2.00x
x = ( )/2.00 =  60.0%
In a fictitious world, element Z has only two isotopes: 35Z with a mass of u and 37Z, with a mass of u. What is the relative abundance of the lighter isotope if the average mass is 35.8 u.
A %, B. 50.0%, C. 60.0%
PAUSE CLICK
Without doing any calculations, we should be able to eliminate choices A and B.
CROSS OUT A and B Why?
Let’s look at Choices B. If the abudance of the lighter isotope is 50%, then the abundance of heavier isotope must be 50% as well.
Remember that percentages add up to 100%. If we have an equal number of isotope 35 and isotope 37, we expect the average
to be 36, which is half-way between 35 and But it’s not 36, it’s 35.8
HIGHLIGHT 35.8 u in the problem
which is less than 36. Since the average is less than the half-way mark, it’s closer to the mass of the lighter isotope.
If it’s closer to the mass of the ligher isotope, we can safely say that the lighter isotope is more abundant.
It can’t be less than 50%. So choice A, 40% is wrong.
The correct answer must be choice C. Let’s verify.
CLICK
Let x be the abundance of the lighter isotope expressed as fraction
CLICK So, isotope 35, which has a mass of atomic mass units has an abundance of x
CLICK And isotope 37, which has a mass of atomic mass unitsh as an abundance of one minus x
The average mass, atomic mass units
HIGHLIGHT u
is equal to
the mass of isotope 35
HIGHLIGHT 35.00u
multiplied by its relative abundance
HIGHLIGHT x
plus the mass of isotope 37
HIGHLIGHT u
HIGHLIGHT 1-x
Solving for x...
CLICK CLICK CLICK CLICK
CLICK we get x equals 0.600, or 60.0 percent.
CLICK PAUSE END RECORDING

2. Video ID: © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08