Final answer:
In the Bohr model, the ratio of the kinetic energy to the potential energy of a hydrogen atom in its n = 4 state can be calculated using the formula Ratio = Kinetic Energy / Potential Energy. The total energy can be determined using the formula Total Energy = -13.6 eV / (n²). The potential energy is equal to the total energy, and the kinetic energy can be calculated by subtracting the potential energy from the total energy.
Step-by-step explanation:
In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the potential energy can be calculated using the formula:
Ratio = Kinetic Energy / Potential Energy
For a hydrogen atom in its n = 4 state, the total energy is given by:
Total Energy = -13.6 eV / (4²)
The potential energy is equal to the total energy, and the kinetic energy can be determined by subtracting the potential energy from the total energy. Therefore:
Kinetic Energy / Potential Energy = (Total Energy - Potential Energy) / Potential Energy
In this case, the hydrogen atom is in the n = 4 state. Therefore, the ratio of KE to PE is:
KE/PE = 1/(4-1) = 1/3
Therefore, the ratio of kinetic energy to potential energy of the hydrogen atom in its n = 4 state is 1:3.