Question

How many silicon-30 atoms are found in this plate?

Answer 1

Hint:1.Silicon (Si) is a nearby relative of \[carbon{\text{ }}\left( C \right)\] in the periodic table.
2.The element could be followed generally in our reality yet isn't found independently in our environment.
3.A silicon Atom involves \[14{\text{ }}electrons\]

Complete step by step answer:Step1: firstly find the volume of plate
Volume of plate with hole
\[V = lmh = 15cm \cdot 12.5cm \cdot 2.5mm = 15cm \cdot 12.5cm \cdot 0.25cm = 46.875c{m^3}\]
We've just been given: the diameter of the hole, which is 2.5 cm, making the sweep 1.25 cm; and the height of the hole, which is 2.50 mm and thus 0.25 cm.
With this data, we can utilize the formula for a cylinder's volume to find the volume of this hole.
\[V = \pi {r^2}h{\text{ }} = \pi {1.25^2}x{\text{ }}0.25 = 1.2272{\text{ }}c{m^3}\;\]
Along these lines, the volume of the plate with the hole in it is unique volume - hole volume
\[ = 46.875c{m^3}\; - 1.2272{\text{ }}c{m^3} = 45.648{\text{ }}cm{3^{}}\]

Step2: Locate the mass of the plate
We know the formula of density
\[d = mv\]
We can adjust that to include volume and density, and have it give us mass. We do this by duplicating the volume variable on the two sides.
\[m = d \cdot v\]
To locate the mass of the plate, we'll use this formula since we've been given the density
\[m{\text{ }} = {\text{ }}d \cdot v{\text{ }} = {\text{ }}8.80g/c{m^3} \cdot 45.648{\text{ }}c{m^3} = {\text{ }}401.701g\]
Step3: Locate the mass of silicon in the plate
The question tells us that the alloy contains \[0.039{\text{ }}\% \] silicon by mass. This implies that in each 1g , there will be \[0.00039g\] of silicon. Thus, the mass of silicon in

\[401.701g\] will be:\[\;0.00039 \cdot 401.701g{\text{ }} = {\text{ }}0.157g\]

Step4: Locate the number of atoms of silicon.
Atoms of Silicon 1 atom of silicon has an atomic mass of \[29.97376{\text{ }}amu\] (which has been given in the question), so that implies 1 mole of silicon will have a mass of\[29.97376{\text{ }}g\] .
The quantity of moles of silicon in \[0.157g\] are:
$\dfrac{{mass{\text{ }}of{\text{ }}sample}}{{mass{\text{ }}of 1 mole}}$ = $\dfrac{{0.157g}}{{29.97376g}}$ = \[0.005238{\text{ }}moles\]
We additionally realize that there are\[\;6.022 \cdot {10^{23}}\] atoms in a mole, so that implies there are \[0.005238 \cdot 6.022 \cdot {10^{23}} = {\text{ }}3.154 \cdot 1021\] atoms in \[0.005238\] moles of silicon .
Step5: Locate the number of atoms of \[silicon - 30\] .
Atoms of \[Silicon - 30\] The question tells us that \[3.10\% \] of silicon atoms are of the \[silicon - 30\] isotope.
 Assuming that this is additionally the situation for our plate, the quantity of silicon30 atoms will be:
\[3.10\% \cdot 3.154 \cdot 1021atoms = 0.0313.15 \cdot 1021atoms{\text{ }} = {\text{ }}9.778 \cdot 1019{\text{ }}atoms\]
The least measure of significant figures in the inquiry is 3, so our answer will have 3 significant figures: \[9.781019atoms.\]

Note:
1.Silicon could be discovered attached to different elements, for example,\[oxygen{\text{ }}\left( O \right)\] .
2.Silicates are the rocks that contain both silicon and oxygen.
3.When decontaminated, it is a grayish crystal that looks metallic.