Question.
If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be placed side by side in a straight line across length of scale of length 20 cm long.
If the diameter of a carbon atom is 0.15 nm, calculate the number of carbon atoms which can be placed side by side in a straight line across length of scale of length 20 cm long.
Solution:
$1 \mathrm{~m}=100 \mathrm{~cm}$
$1 \mathrm{~cm}=10^{-2} \mathrm{~m}$
Length of the scale $=20 \mathrm{~cm}$
$=20 \times 10^{-2} \mathrm{~m}$
Diameter of a carbon atom $=0.15 \mathrm{~nm}$
$=0.15 \times 10^{-9} \mathrm{~m}$
One carbon atom occupies $0.15 \times 10^{-9} \mathrm{~m}$.
$\therefore$ Number of carbon atoms that can be placed in a straight line
$=\frac{20 \times 10^{-2} \mathrm{~m}}{0.15 \times 10^{-9} \mathrm{~m}}$
$=133.33 \times 10^{7}$
$=1.33 \times 10^{9}$
$1 \mathrm{~m}=100 \mathrm{~cm}$
$1 \mathrm{~cm}=10^{-2} \mathrm{~m}$
Length of the scale $=20 \mathrm{~cm}$
$=20 \times 10^{-2} \mathrm{~m}$
Diameter of a carbon atom $=0.15 \mathrm{~nm}$
$=0.15 \times 10^{-9} \mathrm{~m}$
One carbon atom occupies $0.15 \times 10^{-9} \mathrm{~m}$.
$\therefore$ Number of carbon atoms that can be placed in a straight line
$=\frac{20 \times 10^{-2} \mathrm{~m}}{0.15 \times 10^{-9} \mathrm{~m}}$
$=133.33 \times 10^{7}$
$=1.33 \times 10^{9}$
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