Question

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 1

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.