If the density of a certain spherical atomic nucleus is 1.0 x 10¹⁴ g/cm³ and its mass is 3.5 x 10^-23 g, what is the radius in angstroms? (Å= 10⁻¹⁰ m)

• A.
• B.
• C.
• D.
• E.

Answer: (C)

Verified step by step guidance

1. Start by using the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearrange this formula to solve for volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
2. Substitute the given values into the volume formula: \( \text{Volume} = \frac{3.5 \times 10^{-23} \text{ g}}{1.0 \times 10^{14} \text{ g/cm}^3} \).
3. Calculate the volume of the nucleus in cubic centimeters (cm³).
4. Use the formula for the volume of a sphere to find the radius: \( V = \frac{4}{3} \pi r^3 \). Rearrange to solve for the radius: \( r = \left(\frac{3V}{4\pi}\right)^{1/3} \).
5. Convert the radius from centimeters to angstroms using the conversion factor \( 1 \text{ cm} = 10^{8} \text{ Å} \).