Neutron stars are believed to be composed of solid nuclear matter, primarly neutrons. Assuming that a neutron star has the same density as a neutron, calculate the mass (in kg ) of a small piece of a neutron star the size of a spherical pebib with a radius of 0.14 mm . Express your answer using two significant figures.

To calculate the mass of a small piece of a neutron star with a spherical pebble radius of 0.14 mm, we'll follow these steps: 1. **Determine the Density of a Neutron Star:** - Neutron stars have an extremely high density, approximately \( \rho = 1 \times 10^{18} \) kg/m³. 2. **Convert the Radius to Meters:** \[ r = 0.14 \, \text{mm} = 0.14 \times 10^{-3} \, \text{m} = 1.4 \times 10^{-4} \, \text{m} \] 3. **Calculate the Volume of the Sphere:** \[ V = \frac{4}{3}\pi r^3 = \frac{4}{3} \times \pi \times (1.4 \times 10^{-4})^3 \] \[ V \approx \frac{4}{3} \times 3.1416 \times 2.744 \times 10^{-12} \, \text{m}^3 \approx 1.15 \times 10^{-11} \, \text{m}^3 \] 4. **Calculate the Mass:** \[ \text{Mass} = \rho \times V = 1 \times 10^{18} \, \text{kg/m}^3 \times 1.15 \times 10^{-11} \, \text{m}^3 = 1.15 \times 10^7 \, \text{kg} \] 5. **Express the Mass with Two Significant Figures:** \[ \text{Mass} \approx 1.2 \times 10^7 \, \text{kg} \] **Final Answer:** The mass of the small piece is approximately 1.2 × 10⁷ kg.