X-78: mass=78.0 u, abundance = 30.0% QUESTION: In a fictitious world, element X has only two isotopes: 77X with a mass of 77.0 u and 78X, with a mass of 78.0 u. The relative abundance of the heavier isotope is 30.0%. The average mass of the X atoms is... A. 77 u, B. 77.3 u, C. 77.5 u, D. 78 u X-78: mass=78.0 u, abundance = 30.0% X-77: mass=77.0 u, abundance = 70.0% Average Mass = (0.300)(78.0 u) + (0.700)(77.0 u) = 77.3 u; closer to mass of more abundant isotope In a fictitious world, element X has only two isotopes: 77X with a mass of 77.0 u and 78X, with a mass of 78.0 u. The relative abundance of the heavier isotope is 30.0%. The average mass of the X atoms is... A. 77 u, B. 77.3 u, C. 77.5 u, D. 78 u PAUSE CLICK Without doing any calculations, we should be able to eliminate choices A, C, and D. CROSS OUT A, C, and D Why? Let’s look at Choices A and D. Since we have significant amounts of isotopes 77 and 78, the average must be between 77 and 78 atomic mass units. What about choice C? 77.5 is exactly half-way between 77 and 78. This would be the average if we have equal amounts of both isotopes. We don’t. We have more of the ligher isotope. CLICK The relative abundance of the heavier isotope is 30%. CLICK This means that the relative abundance of the lighter isotope is 70%. Remember that percentages should add up to 100%. Since the ligher isotope is more abundant, we expect the average to be closer to the mass of the ligher isotope. That is the case in choice B. It’s not half-way between 77 and 78. It’s closer to 77. The correct answer is B. Let’s verify that the value in choice B is correct. We can look up isotopic abundance for Mg and find the following: CLICK The Average Mass is equal to ... the mass of isotope 78 HIGHLIGHT 78.0u multiplied by its relative abundance HIGHLIGHT 0.300 plus the mass of isotope 77 HIGHLIGHT 77.0 u HIGHLIGHT 0.700 If we did this, we get 77.3 atomic mass units. CLICK PAUSE END RECORDING

Video ID: 4-1-2 © 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