
A silicon chip used in an integrated circuit of a microcomputer has a mass of 5.68 mg. How many silicon atoms are present in this chip? (atomic mass of Si = 28.08)
(A)- $6.02\times {{10}^{23}}$
(B)- $5.68\times {{10}^{23}}$
(C)- $1.22\times {{10}^{20}}$
(D)- $11.36\times {{10}^{23}}$
Answer
486.9k+ views
Hint: In order to find the number of atoms present in the chip, from the given mass, the moles can be calculated. And as in a mole, the number of atoms is equal to the Avogadro’s number. So, we can then find the number of atoms in the given mass (or moles).
Complete step by step solution:
It is given that the silicon chip used has a mass of \[5.68\,mg=5.68\times {{10}^{-3}}g\] . Then, we can find the moles of silicon present in the chip by, $\text{number of moles=}\dfrac{\text{mass}}{\text{molar mass}}$ .
It is given that the atomic mass of silicon is 28.08 g. So, its molar mass is 28.08 g/mol.
Then, the moles of silicon used is $\text{=}\dfrac{5.68\times {{10}^{-3}}\,}{28.08}=2.022\times {{10}^{-4}}\,moles$
As in one mole of silicon substance, we have $6.022\times {{10}^{23}}$ silicon atoms. Then, in $2.022\times {{10}^{-4}}$ moles, the number of silicon atoms present will be $(2.022\times {{10}^{-4}}\times 6.022\times {{10}^{23}})\,$$=1.218\times {{10}^{20}}\approx 1.22\times {{10}^{20}}$ atoms of silicon.
Therefore, the number of silicon atoms present in the chip used is option (C)- $1.22\times {{10}^{20}}$.
Additional information:
The silicon is used in the chips of integrated circuits used in microprocessors, in diodes and also transistors because being a semiconductor, it operates at a high temperature and thus not easily damaged. And due to its abundance in nature, it is less expensive and it has a very high purity which makes it suitable for electronic devices.
Note: The number $6.022\times {{10}^{23}}$ is the number of atoms present in a mole is called as the Avogadro’s number, ${{N}_{A}}$. Also, the mass given is not in SI units, so the unit conversion must be done carefully, to get both the mass and the molar mass in the same units.
Complete step by step solution:
It is given that the silicon chip used has a mass of \[5.68\,mg=5.68\times {{10}^{-3}}g\] . Then, we can find the moles of silicon present in the chip by, $\text{number of moles=}\dfrac{\text{mass}}{\text{molar mass}}$ .
It is given that the atomic mass of silicon is 28.08 g. So, its molar mass is 28.08 g/mol.
Then, the moles of silicon used is $\text{=}\dfrac{5.68\times {{10}^{-3}}\,}{28.08}=2.022\times {{10}^{-4}}\,moles$
As in one mole of silicon substance, we have $6.022\times {{10}^{23}}$ silicon atoms. Then, in $2.022\times {{10}^{-4}}$ moles, the number of silicon atoms present will be $(2.022\times {{10}^{-4}}\times 6.022\times {{10}^{23}})\,$$=1.218\times {{10}^{20}}\approx 1.22\times {{10}^{20}}$ atoms of silicon.
Therefore, the number of silicon atoms present in the chip used is option (C)- $1.22\times {{10}^{20}}$.
Additional information:
The silicon is used in the chips of integrated circuits used in microprocessors, in diodes and also transistors because being a semiconductor, it operates at a high temperature and thus not easily damaged. And due to its abundance in nature, it is less expensive and it has a very high purity which makes it suitable for electronic devices.
Note: The number $6.022\times {{10}^{23}}$ is the number of atoms present in a mole is called as the Avogadro’s number, ${{N}_{A}}$. Also, the mass given is not in SI units, so the unit conversion must be done carefully, to get both the mass and the molar mass in the same units.
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