Questions: The diameter of a proton is about 1.9 × 10^-15 meters. A hydrogen atom has an overall length of 100,000 times (or 1 × 10^5 times) the diameter of a proton. What is the length of the hydrogen atom, in meters, if it were written in scientific notation? 1.9 × 10^-8 meters 1.9 × 10^-12 meters 1.9 × 10^-15 meters 1.9 × 10^-10 meters

The diameter of a proton is about 1.9 × 10^-15 meters. A hydrogen atom has an overall length of 100,000 times (or 1 × 10^5 times) the diameter of a proton.

What is the length of the hydrogen atom, in meters, if it were written in scientific notation?
1.9 × 10^-8 meters
1.9 × 10^-12 meters
1.9 × 10^-15 meters
1.9 × 10^-10 meters

Transcript text: The diameter of a proton is about $1.9 \times 10^{-15}$ meters. A hydrogen atom has an overall length of 100,000 times (or $1 \times 10^{5}$ times) the diameter of a proton. What is the length of the hydrogen atom, in meters, if it were written in scientific notation? $1.9 \times 10^{-8}$ meters $1.9 \times 10^{-12}$ meters $1.9 \times 10^{-15}$ meters $1.9 \times 10^{-10}$ meters

Solution

Solution Steps

Step 1: Given Values

The diameter of a proton is given as: \[ d = 1.9 \times 10^{-15} \text{ meters} \] The hydrogen atom is stated to be $1 \times 10^{5}$ times the diameter of a proton.

Step 2: Calculate the Length of the Hydrogen Atom

To find the length of the hydrogen atom $L$, we multiply the diameter of the proton by the factor: \[ L = d \times 1 \times 10^{5} \] Substituting the value of $d$: \[ L = 1.9 \times 10^{-15} \times 1 \times 10^{5} \]

Step 3: Simplify the Expression

Using the rules of multiplying numbers in scientific notation, we add the exponents: \[ L = 1.9 \times 10^{-15 + 5} = 1.9 \times 10^{-10} \text{ meters} \]