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?

A. 3.2 × 10^-¹⁰ m
B. 3.2 × 10^-⁹ m
C. 2.72 × 10^-¹⁰ m
D. 3.2 × 10^-¹¹ m

1 answer

To find the difference between the sizes of these atoms, we need to subtract their sizes.

The size of a hydrogen atom is 1.2 × 10^-¹⁰ m and the size of an oxygen atom is 0.000000000152 m.

To do the subtraction, we need to express the sizes in scientific notation with the same exponent.

1.2 × 10^-¹⁰ m = 1.2 × 10^-¹⁰ m
0.000000000152 m = 1.52 × 10^-10 m (to express it in scientific notation, we move the decimal point 10 places to the left to get a number between 1 and 10).

Now we can subtract them:

1.52 × 10^-10 m - 1.2 × 10^-¹⁰ m = (1.52 - 1.2) × 10^-¹⁰ m = 0.32 × 10^-¹⁰ m

To express it in scientific notation, we need to move the decimal point to get a number between 1 and 10:

0.32 × 10^-¹⁰ m = 3.2 × 10^-¹¹ m

The difference between the sizes of these atoms in scientific notation is option D, 3.2 × 10^-¹¹ m.