Question

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

Answer 1

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.