Question

a. what is the average atomic mass of this element? b. use your periodic table to determine which element this is. 48.7% have a mass of 74.61 amu, and 22.2% have a mass of 75.20 amu. 24.1% of all the isotopes have a mass of

Explanation:

Step1: Convert percentages to decimals

$48.7\% = 0.487$, $24.1\%=0.241$, $22.2\% = 0.222$

Step2: Calculate the contribution of each isotope to the average atomic mass

Let the masses of the isotopes be $m_1 = 74.61$ amu, $m_2$ (unknown for now), $m_3=75.20$ amu.
The contribution of the first isotope is $0.487\times74.61 = 36.33507$ amu.
The contribution of the second isotope is $0.241\times m_2$.
The contribution of the third isotope is $0.222\times75.20=16.6944$ amu.
Assume the remaining percentage $1-(0.487 + 0.241+0.222)=0.05$ has an isotope mass $m_4$ (not given in the problem - assuming no other significant isotopes for simplicity). Its contribution is $0.05\times m_4$. For simplicity, if we ignore the $5\%$ (since no data about it), the average atomic mass $A$ is:
$A=0.487\times74.61+0.241\times m_2 + 0.222\times75.20$. Since we assume no other significant isotopes, $A=0.487\times74.61+0.241\times m_2+0.222\times75.20=36.33507+0.241\times m_2 + 16.6944$. If we assume the $m_2$ - related part is negligible (as no data), $A = 36.33507+16.6944=74.82947\approx74.83$ amu

Step3: Identify the element from the periodic table

Looking at the periodic table, the element with an average atomic mass close to $74.83$ amu is Arsenic (As) which has an average atomic mass of approximately 74.92 amu.

Answer:

a. Approximately 74.83 amu
b. Arsenic (As)