Question

calculate the average atomic mass of silver if 13 out of 25 atoms are silver - 107 and 12 out of 25 atoms are silver - 109. a student believed that she had discovered a new element! analysis found it contained two isotopes. the isotopes were: 19.9% with an atomic mass of 10.013 and 80.1% with an atomic mass of 11.009. what is the average atomic mass, and do you think the student discovered a new element? explain!

Explanation:

Step1: Calculate the contribution of silver - 107

The fraction of silver - 107 is $\frac{13}{25}=0.52$. Its contribution to the average atomic mass is $0.52\times107 = 55.64$.

Step2: Calculate the contribution of silver - 109

The fraction of silver - 109 is $\frac{12}{25}=0.48$. Its contribution to the average atomic mass is $0.48\times109 = 52.32$.

Step3: Calculate the average atomic mass

Add the two contributions together: $55.64 + 52.32=107.96$.

Step1: Calculate the average atomic mass

The average atomic mass formula is $m=\sum_{i}x_im_i$, where $x_i$ is the fractional abundance and $m_i$ is the atomic mass of the isotope.
The fractional abundance of the first isotope $x_1 = 0.199$ and $m_1=10.013$, and the fractional abundance of the second isotope $x_2 = 0.801$ and $m_2 = 11.009$.
$m=(0.199\times10.013)+(0.801\times11.009)$
$m = 1.992587+8.818209$
$m=10.810796\approx10.81$

Step2: Determine if it's a new element

The average atomic mass of 10.81 is close to the average atomic mass of boron (10.811). So, the student did not discover a new element.

Answer:

$107.96$

For the second - part of the problem: