Final answer:
In the n = 3 state of a hydrogen atom, the electron's velocity, kinetic energy, and potential energy can be determined using the Bohr model equations. The electron's energy levels within the atom are quantized and depend on the principal quantum number, n.
Step-by-step explanation:
Understanding the Hydrogen Atom in the n = 3 State
Using the Bohr model of the hydrogen atom, it is possible to calculate various properties of an electron when it is in a particular orbit defined by a principal quantum number, n. For the n = 3 state of a hydrogen atom, we can determine the electron’s velocity, its kinetic energy, and its potential energy.
a) Electron’s Velocity in n = 3 State
The velocity of an electron in a Bohr orbit is given by the formula v = Zke^2/(nh), where Z is the atomic number (1 for hydrogen), k is Coulomb's constant, e is the charge of the electron, n is the principal quantum number, and h is Planck's constant. For hydrogen (Z=1) in the n = 3 state, substituting the constants into the equation gives the velocity.
b) Kinetic Energy of the Electron
The kinetic energy (KE) of an electron in a Bohr orbit can be calculated using KE = 0.5m_ve^2, where m_e is the mass of the electron and v is the velocity as determined in part (a).
c) Potential Energy of the Electron
The potential energy (PE) for an electron in a Bohr orbit is given by PE = -ke^2/(r), where r is the radius of the orbit, which can be found using the Bohr model.
d) Energy Levels of Electrons in Hydrogen
The energy levels of an electron in a hydrogen atom are quantized, and they depend on the principal quantum number n. The energy level can be calculated using the formula En = -13.6eV/n^2, where -13.6 eV is the energy of the ground state (n=1) for hydrogen. The electron is less tightly bound at higher values of n.