Question

Andy uses his calculator to find how much larger the radius of a gold atom is than the radius of a helium atom. The calculator shows the difference as 1.43 × 10^(-8). What is the difference in centimeters written in scientific notation?

a) 1.43 × 10^(-8) cm
b) 2.07 × 10^(-9) cm
c) 1.43 × 10^(-15) cm
d) 2.07 × 10^(-15) cm

Answer 1

The difference in the radii of a gold atom and a helium atom is 1.43 × 10^{-8} meters. To convert this to centimeters, you multiply by 100, which gives 1.43 × 10^{-6} centimeters. There may be an error in the provided choices as this option is not listed.

Step-by-step explanation:

Andy's calculator displays the difference in radii as 1.43 × 10^{-8} meters. Since the question asks for the difference in centimeters, we need to convert meters to centimeters. We know that 1 meter is equal to 100 centimeters, so we use this fact to convert the given measurement from meters to centimeters.

To convert meters to centimeters, we multiply the given number by 100:

1. Write the given difference: 1.43 × 10^{-8} meters
2. Convert meters to centimeters: 1.43 × 10^{-8} meters × 100 centimeters/meter
3. Apply the conversion: 1.43 × 100 × 10^{-8} = 1.43 × 10^{-6} centimeters

Therefore, the difference in the radii of a gold atom and a helium atom in centimeters, written in scientific notation, is 1.43 × 10^{-6} cm. Since this option is not present among the choices given, there seems to be an error in the question or the options provided.