calculate the average atomic mass of silver if 13 out of 25 atoms are silver - 107 and 12 out of 25 atoms…
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!
Answer
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: $55.64 + 52.32=107.96$.
Answer:
$107.96$
For the second - part of the problem:
Explanation:
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:
The average atomic mass is approximately $10.81$. The student did not discover a new element because the calculated average atomic mass is close to that of boron.