To make a large-scale representation of a hydrogen atom in its ground state, you start with a super ball (D=3.78 cm) to represent the nucleus. How far away, R, in km will you have to put the representation electron?
To determine the distance at which you need to place the representation electron from the super ball nucleus, we can use the Bohr model of the hydrogen atom.
The Bohr model states that the electron orbits the nucleus in discrete energy levels, and the distance between the nucleus and the electron depends on the energy level. The ground state of a hydrogen atom is the lowest energy level, where the electron is closest to the nucleus.
The ground state of a hydrogen atom has a specific radius referred to as the Bohr radius (a₀), which is approximately 0.529 Å (angstroms) or 0.529 x 10^(-10) meters.
To convert this radius from meters to kilometers, we divide by 1000:
a₀ = 0.529 x 10^(-10) meters
a₀ = 0.529 x 10^(-13) kilometers
Now, let's assume the super ball represents the nucleus, and you want to place the representation electron at the distance corresponding to the Bohr radius.
R = Bohr radius = 0.529 x 10^(-13) kilometers
R ≈ 5.29 x 10^(-14) kilometers
Therefore, you would have to place the representation electron approximately 5.29 x 10^(-14) kilometers away from the super ball nucleus to represent a hydrogen atom in its ground state.