Question

silicon is the second most abundant element in earth - crust. it is used in the electronics industry to manufacture transistors, and in the construction industry to produce concrete and portland cement. the following graph shows the relative abundances of the silicon isotopes. an image of a pie chart is shown, there are three wedges. the largest wedge is labeled as si - 28 and it is at 92.22%. the second wedge is labeled as si - 29 and it is at 4.68%. the smallest wedge is labeled si - 30 and it is at 3.09%. what could be the estimated atomic mass of silicon? 26.2 amu 28.1 amu 29.8 amu

Explanation:

Step1: Recall atomic - mass formula

The atomic mass of an element with isotopes is calculated as the weighted - average of the masses of its isotopes. The formula is $A=\sum_{i}m_i\times p_i$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is its relative abundance. For silicon isotopes, $m_{Si - 28}=28$, $m_{Si - 29}=29$, $m_{Si - 30}=30$, $p_{Si - 28}=0.9222$, $p_{Si - 29}=0.0468$, $p_{Si - 30}=0.0309$.

Step2: Calculate the weighted - average

$A = 28\times0.9222+29\times0.0468 + 30\times0.0309$
$A=28\times0.9222+29\times0.0468+30\times0.0309=25.8216+1.3572 + 0.927$
$A=28.1058\approx28.1$ amu

Answer:

28.1 amu