Questions: One of the particles in an atom is the proton. A proton has a radius of approximately 1.0 x 10^-13 cm and a mass of 1.7 x 10^-24 g. Part A Determine the density of a proton. (Hint: Find the volume of the proton and then divide the mass by the volume to get the density.) (volume of a sphere = 4/3 pi r^3 ; pi=3.14 ) Express your answer to two significant figures and include the appropriate units.

Solution Steps

The volume \( V \) of a sphere is given by the formula: \[ V = \frac{4}{3} \pi r^3 \] Given the radius \( r = 1.0 \times 10^{-13} \) cm and \( \pi = 3.14 \), we can substitute these values into the formula: \[ V = \frac{4}{3} \times 3.14 \times (1.0 \times 10^{-13})^3 \] \[ V = \frac{4}{3} \times 3.14 \times 1.0 \times 10^{-39} \] \[ V = 4.1867 \times 10^{-39} \text{ cm}^3 \]

Density \( \rho \) is defined as mass \( m \) divided by volume \( V \): \[ \rho = \frac{m}{V} \] Given the mass \( m = 1.7 \times 10^{-24} \) g and the volume \( V = 4.1867 \times 10^{-39} \) cm\(^3\), we can substitute these values into the formula: \[ \rho = \frac{1.7 \times 10^{-24}}{4.1867 \times 10^{-39}} \] \[ \rho = 4.060 \times 10^{14} \text{ g/cm}^3 \]

Final Answer