The size of a hydrogen atom is about 1.2 × 10^−10 m across. The size of an oxygen atom is 0.000000000152 m across. What is the difference between the sizes of these atoms in scientific notation?

Question

A: 3.2 X 10^-9 m
B: 2.72 X 10^-10 m
C: 3.2 X 10^-11 m
D: 3.2 X 10^-10 m

Answer 1

To find the difference between the sizes of the atoms, we need to subtract the size of the hydrogen atom from the size of the oxygen atom.

0.000000000152 m - 1.2 × 10^-10 m = 1.52 × 10^-10 m - 1.2 × 10^-10 m.

To subtract these numbers, we need to make sure they have the same exponent, so we need to convert 1.52 × 10^-10 m to scientific notation with the same exponent as 1.2 × 10^-10 m.

1.52 × 10^-10 m = 0.152 × 10^-9 m.

Now, we can subtract the numbers:

0.152 × 10^-9 m - 1.2 × 10^-10 m = 0.152 × 10^-9 m - 0.12 × 10^-9 m.

We subtract the numbers, keeping the same exponent:

0.152 × 10^-9 m - 0.12 × 10^-9 m = (0.152 - 0.12) × 10^-9 m.

0.152 - 0.12 = 0.032.

So, the difference between the sizes of these atoms is 0.032 × 10^-9 m.

Writing this in scientific notation:

0.032 × 10^-9 m = 3.2 × 10^-11 m.

Therefore, the difference is C: 3.2 × 10^-11 m.