Neutron stars are believed to be composed of solid nuclear mather, primarily neutrons. Correct Part B 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 pebble wh a radius of 0.14 mm . Express your answer using two significant figures. \( \sqrt{0} \) Az ? \( x^{3} \) \( x_{b} \) \( \frac{4}{b} \) \( \sqrt{x} \) \( \sqrt[3]{x} \) \( \bar{x} \) \( \hat{x} \) (0) \( x \cdot 10^{n} \)

To calculate the mass of a small piece of a neutron star the size of a spherical pebble with a radius of 0.14 mm, we'll follow these steps: ### 1. **Determine the Density of a Neutron Star** Neutron stars are incredibly dense objects. For this calculation, we'll use the approximate density of nuclear matter, which is about: \[ \rho = 2.3 \times 10^{17} \, \text{kg/m}^3 \] ### 2. **Calculate the Volume of the Pebble** The pebble is a sphere with a radius \( r = 0.14 \, \text{mm} = 0.14 \times 10^{-3} \, \text{m} \). The volume \( V \) of a sphere is given by: \[ V = \frac{4}{3} \pi r^3 \] Plugging in the values: \[ V = \frac{4}{3} \pi (0.14 \times 10^{-3})^3 \\ V \approx \frac{4}{3} \times 3.1416 \times (2.744 \times 10^{-12}) \\ V \approx 11.5 \times 10^{-12} \, \text{m}^3 \] ### 3. **Calculate the Mass** Mass \( m \) is the product of density \( \rho \) and volume \( V \): \[ m = \rho \times V \] Substituting the known values: \[ m = 2.3 \times 10^{17} \, \text{kg/m}^3 \times 11.5 \times 10^{-12} \, \text{m}^3 \\ m \approx 2.6485 \times 10^{6} \, \text{kg} \] ### 4. **Express the Answer with Two Significant Figures** Rounding to two significant figures: \[ m \approx 2.6 \times 10^{6} \, \text{kg} \] **Final Answer:** The mass of the pebble is approximately \( 2.6 \times 10^{6} \) kg.