Question

read the passage and use the diagram to answer the next question. silicon is the second most abundant element in earths 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 naturally occurring silicon isotopes. 8. what could be the estimated atomic mass of silicon?

Explanation:

Step1: Calculate the contribution of each isotope

The atomic mass of an isotope is approximately equal to its mass number. For \(Si - 28\) (mass number \(A_{28}=28\)), its abundance \(x_{28}=92.22\%=0.9222\). The contribution of \(Si - 28\) is \(28\times0.9222\).

$$28\times0.9222 = 25.8216$$

For \(Si - 29\) (mass number \(A_{29} = 29\)), its abundance \(x_{29}=4.68\%=0.0468\). The contribution of \(Si - 29\) is \(29\times0.0468\).

$$29\times0.0468=1.3572$$

For \(Si - 30\) (mass number \(A_{30}=30\)), its abundance \(x_{30}=3.09\%=0.0309\). The contribution of \(Si - 30\) is \(30\times0.0309\).

$$30\times0.0309 = 0.927$$

Step2: Sum up the contributions

The atomic mass of silicon \(M\) is the sum of the contributions of each isotope.

$$M=25.8216 + 1.3572+0.927$$

$$M=28.1058\approx28.11$$

Answer:

\(28.11\)