What is the velocity of an electron in ground state?

Asked by Chetan | 9th Feb, 2012, 01:42: AM

Expert Answer:

Bohr postulated that electron orbits about the nucleus are quantized.

When electrons orbit the nucleus in more distant orbits, they have more total energy. Bohr called possible electron orbits energy levels or stationary states. In Bohr's model energy levels are quantized. Only specific discrete energy levels are possible. The lowest energy level is the ground state, and higher energy levels are the first, second, etc. excited states. As long as the electrons are in one of these quantized energy levels or stationary states they orbit the nucleus and remain stable without emitting electromagnetic radiation and losing energy.Electrons can jump up or down between energy levels, but cannot have energy values between the allowed energy levels. There are no fractional energy levels.

Electrons jumping between energy levels explains spectral lines.

When an electron jumps to a higher energy level, it must get the extra energy from somewhere. One way is by colliding with another atom, leading to collisional excitation. Another way is by absorbing a photon of light. Both photons and energy levels are quantized. When a photon's energy equals the energy difference between energy levels and it strikes an electron, the electron absorbs the photon and jumps to the higher level. This process causes absorption line spectra.

When a photon is in an excited state, either from collisional excitation or from having previously absorbed a photon, it can jump to a lower level. The electron rids itself of the extra energy by emitting a photon having the right amount of energy. An emission line spectrum results.

Each type of atom has its own unique set of spectral lines because it has its own unique set of energy levels.

The total energy is the sum of the electron's kinetic energy and the potential energy coming from the electron-proton interaction.

The kinetic energy is given by KE = 1/2 mv2.

This can be found by analyzing the force on the electron. This force is the Coulomb force; because the electron travels in a circular orbit, the acceleration will be the centripetal acceleration:

The potential energy, on the other hand, is PE = - k e2 / r. Note that the potential energy is twice as big as the kinetic energy, but negative. This relationship between the kinetic and potential energies is valid not just for electrons orbiting protons, but also in gravitational situations, such as a satellite orbiting the Earth.

The total energy is: 
KE + PE = -1/2 ke2 / r = - 1/2 (8.99 x 109)(1.60 x 10-19) / 5.29 x 10-11

This works out to -2.18 x 10-18 J. This is usually stated in energy units of electron volts (eV). An eV is 1.60 x 10-19 J, so dividing by this gives an energy of -13.6 eV. To remove the electron from the atom, 13.6 eV must be put in; 13.6 eV is thus the ionization energy of a ground-state electron in hydrogen.

Answered by  | 9th Feb, 2012, 09:40: AM

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