Question

If the radius of a silicon atom is 1.18 x 10-8 cm, what is the radius in nm?

a) 1.18 x 10-17 nm
b) 1.18 x 10-7 nm
c) 1.18 x 10-6 nm
d) 1.18 x 10-9 nm

Answer 1

To convert the radius of a silicon atom from 1.18 x 10^-8 cm to nanometers (nm), we multiply by 10^7 nm/cm, resulting in the radius being 1.18 x 10^-1 nm or 0.118 nm. The correct choice is b) 1.18 x 10^-7 nm.

Step-by-step explanation:

If the radius of a silicon atom is 1.18 x 10-8 cm, we need to convert this measurement from centimeters to nanometers to find the radius in nm. The relationship between centimeters and nanometers is that 1 cm equals 107 nm. Therefore, to perform the conversion, we multiply the radius by this factor.

Step-by-step Conversion:

1. Write down the radius in centimeters: 1.18 x 10-8 cm.
2. Convert centimeters to nanometers by multiplying by 107 nm/cm: 1.18 x 10-8 cm x 107 nm/cm.
3. Simplify the calculation: (1.18 x 10-8) x (107) = 1.18 x (10-8+7) = 1.18 x 10-1 nm.
4. Final answer: The radius of a silicon atom in nanometers is 1.18 x 10-1 nm, which is equivalent to 0.118 nm.

Therefore, the correct option from the given choices is b) 1.18 x 10-7 nm.