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Question: A silicon chip used in an integrated circuit of a microcomputer has a mass of 5.68 mg. How many sili...

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)- 6.02×10236.02\times {{10}^{23}}
(B)- 5.68×10235.68\times {{10}^{23}}
(C)- 1.22×10201.22\times {{10}^{20}}
(D)- 11.36×102311.36\times {{10}^{23}}

Explanation

Solution

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=5.68×10−3g5.68\,mg=5.68\times {{10}^{-3}}g . Then, we can find the moles of silicon present in the chip by, number of moles=massmolar mass\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 =5.68×10−3 28.08=2.022×10−4 moles\text{=}\dfrac{5.68\times {{10}^{-3}}\,}{28.08}=2.022\times {{10}^{-4}}\,moles
As in one mole of silicon substance, we have 6.022×10236.022\times {{10}^{23}} silicon atoms. Then, in 2.022×10−42.022\times {{10}^{-4}} moles, the number of silicon atoms present will be (2.022×10−4×6.022×1023) (2.022\times {{10}^{-4}}\times 6.022\times {{10}^{23}})\, =1.218×1020≈1.22×1020=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)- 1.22×10201.22\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 6.022×10236.022\times {{10}^{23}} is the number of atoms present in a mole is called as the Avogadro’s number, NA{{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.