Estimate the mass of a nucleus with radius $2.8 \times 10 ^ { - 15 } \mathrm {~m} . \left( 1 \mathrm { u } = 1.6605 \times 10 ^ { - 27 } \mathrm {~kg} \right)$
A) about $2.1 \times 10 ^ { - 26 } \mathrm {~kg}$
B) about $4.7 \times 10 ^ { - 26 } \mathrm {~kg}$
C) about $2.3 \times 10 ^ { - 26 } \mathrm {~kg}$
D) about $7.5 \times 10 ^ { - 27 } \mathrm {~kg}$

Question

Quizplus · Accepted Answer

The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$. The density of nuclear matter is approximately constant, so the mass of the nucleus is proportional to its volume. Therefore, the mass of the nucleus is:$$m = \rho V = \rho \frac{4}{3} \pi r^3$$where $\rho$ is the density of nuclear matter. The density of nuclear matter is approximately $2.3 \times 10^{17} \mathrm{~kg/m^3}$. Therefore, the mass of the nucleus is:$$m = (2.3 \times 10^{17} \mathrm{~kg/m^3}) \frac{4}{3} \pi (2.8 \times 10^{-15} \mathrm{~m})^3 \approx 2.1 \times 10^{-26} \mathrm{~kg}$$

Estimate the Mass of a Nucleus with Radius 2.8×10−15 m.(1u=1.6605×10−27 kg)2.8 \times 10 ^ { - 15 } \mathrm {~m} . \left( 1 \mathrm { u } = 1.6605 \times 10 ^ { - 27 } \mathrm {~kg} \right)2.8×10−15 m.(1u=1.6605×10−27 kg)

Estimate the Mass of a Nucleus with Radius $2.8 \times 10 ^ { - 15 } \mathrm {~m} . \left( 1 \mathrm { u } = 1.6605 \times 10 ^ { - 27 } \mathrm {~kg} \right)$