Question

The nucleus of the hydrogen atom has a radius of about 1 × 10⁻¹⁵ m. The electron is normally found at a distance of about 5.3 × 10⁻¹¹ m from the nucleus.

How many times farther from the center is the electron than the radius of the nucleus?

Answer and Detailed Explanation

Step 1: Understand the Given Data

• Radius of hydrogen nucleus: r_nucleus = 1 × 10⁻¹⁵ m
• Distance of electron (Bohr radius): r_electron = 5.3 × 10⁻¹¹ m

Step 2: Form the Ratio

To find how many times farther the electron is from the nucleus, we compute:
Ratio = r_electron / r_nucleus = (5.3 × 10⁻¹¹) / (1 × 10⁻¹⁵)

Step 3: Simplify the Expression

Use the rule of exponents:
= 5.3 × 10^(−11 − (−15)) = 5.3 × 10⁴

Therefore, the electron is approximately 53,000 times farther from the center than the radius of the nucleus.

Conclusion

This vast difference in scale illustrates why the atom is considered to be mostly empty space. The tiny nucleus occupies an almost negligible volume compared to the entire atom.