Question

From the information in this chapter on the mass of the proton, the mass of the electron, and the sizes of the nucleus and the atom, calculate the densities of a hydrogen nucleus and a hydrogen atom.

Short answer

The densities of a hydrogen nucleus and a hydrogen atom can be calculated using the following information: - Proton mass (m_p): \(1.67 \times 10^{-27}\) kg - Electron mass (m_e): \(9.11 \times 10^{-31}\) kg - Nucleus size (r_p): \(1.2 \times 10^{-15}\) m - Atom size (r_a): \(5.3 \times 10^{-11}\) m By using the sphere volume formula and calculating the mass of the hydrogen atom (m_a = m_p + m_e), the densities are found as follows: - Hydrogen nucleus density (ρ_p) = \(m_p / V_p\) - Hydrogen atom density (ρ_a) = \(m_a / V_a\)

Step-by-step solution

1. Mass of proton, mass of electron, and sizes of the nucleus and atom

We will be using the following constants: Mass of proton (m_p): 1.67 x 10^{-27} kg Mass of electron (m_e): 9.11 x 10^{-31} kg Size of the nucleus (r_p): 1.2 x 10^{-15} m (approx.) Size of the hydrogen atom (r_a): 5.3 x 10^{-11} m (approx.)

2. Calculate the volume of the hydrogen nucleus and the hydrogen atom

We can calculate the volume of the hydrogen nucleus and hydrogen atom using the formula for the volume of a sphere: Volume of hydrogen nucleus (V_p) = (4/3) * π * r_p^3 Volume of hydrogen atom (V_a) = (4/3) * π * r_a^3

3. Calculate the mass of the hydrogen atom

The mass of the hydrogen atom (m_a) is the sum of the mass of the proton and the mass of the electron: m_a = m_p + m_e

4. Calculate the densities of hydrogen nucleus and hydrogen atom

Now, we can calculate the densities of the hydrogen nucleus and hydrogen atom using the formula density = mass/volume: Density of hydrogen nucleus (ρ_p) = m_p / V_p Density of hydrogen atom (ρ_a) = m_a / V_a