Question

solve the following isotope related question
a) the former president and vice president have just simultaneously discovered new elements. they decided to have a contest to see which element had the greater atomic mass based on the abundance of their respective isotopes. who wins the contest?
isotope atomic mass abundance
bidenium - 36 36.013 amu 8.02%
bidenium - 37 36.9 amu 13%
bidenium - 40 39.87 amu 78.98%
isotope atomic mass abundance
harrisium - 39 38.8 amu 93.11%
harrisium - 43 43.46 amu 6.89%

Explanation:

Step1: Calculate average atomic mass of Bidenium

The formula for average atomic mass $A = \sum_{i = 1}^{n}m_i\times p_i$, where $m_i$ is the atomic - mass of isotope $i$ and $p_i$ is the percentage abundance of isotope $i$ (in decimal form).
For Bidenium:
$p_1=0.0802$, $m_1 = 36.013$ amu; $p_2 = 0.13$, $m_2=36.9$ amu; $p_3 = 0.7898$, $m_3 = 39.87$ amu.
$A_{Bidenium}=36.013\times0.0802+36.9\times0.13 + 39.87\times0.7898$
$A_{Bidenium}=36.013\times0.0802+36.9\times0.13+39.87\times0.7898$
$=2.8882426+4.797+31.404626$
$=39.09$ amu

Step2: Calculate average atomic mass of Harrisium

For Harrisium:
$p_1 = 0.9311$, $m_1=38.8$ amu; $p_2 = 0.0689$, $m_2 = 43.46$ amu.
$A_{Harrisium}=38.8\times0.9311+43.46\times0.0689$
$A_{Harrisium}=38.8\times0.9311 + 43.46\times0.0689$
$=36.12668+2.994494$
$=39.12$ amu

Answer:

Harrisium wins the contest.