Binding energy of electron in atom - Structure of matter Flashcards
What is the binding energy of a particle in a system?
The binding energy of a particle in a system generally equals the work that must be done to take off the particle out of the system.
Therefore, the binding energy of an electron equals the energy that must be supplied to remove the electron from the action of electrostatic forces of the nucleus.
I.e. to remove it to the place of the zero potential energy.
The totaly energy E of the electron in the field of a nucleus is negative (see equation 1.12 in book) and its highest value is 0 (for n –> infinity and also simultaneously for r –> infinity) (see equation 1.18 in book) at infinite distance from nucleus.
Therefore, the binding energy Eb in this system is determined from the condition
Eb + E = 0
and hence
Eb = -E
Describe the binding energy in heavy atoms.
The binding energy of an electron in the field of a nucleus numerically equals its total energy given by equation 1.12 (see book) and it is positive.
For heavy atoms, other factos appears in this equation, since the total energy is also a function of the atomic number Z.
Due to this fact, binding eneries of electron in these atoms are Z2 times higher for the same n.
Thus, the binding energy of an electron in the K-shell of the hydrogen atom is -(-13.6eV) = 13.6eV while in the atom of uranium (Z=92) in the same shell it is of order of magnitude 105eV (922 times higher).
What is the ionization potential?
The binding energy is also called the ionisation potential.
There are various values of the ionisation potential for electrons in heavy atoms since these electrons possess different total energies.
Naturally, the lowest value of the ionisation appertains to the valence electrons.
If an electron gets energy higher than its binding energy due to absorption of quantum of radiation of energy, hf, some part of this energy is consumed forthe work which must be done to remove this electron from the system and the remaining part appears as the kinetic energy of the removed electron.
Thus the law o energy conservation directly presents the well known Einstein’s quation for the photoeffect:
hf = Eb + (1/2)mv2
Explain ionised atoms in this context.
A positively charged ion is formed from an atom by the ionisation, since positive charge of nucleus prevails.
The ionisation of the atom also increases the total energy of the system (since the presence of electron in the system decreased its total energy; the sign of the total energy of the electron is negative).
Therefore, an ionised atom is not stale and it tends to return back intot eh ground state with the minimum energy by the emission of the fluorescence radiation.
What are the changes in the electron envelope after energy absorption?
Changes occuring in the electron envelope of the nucleus after the energy absorption depends on its amount.
if the absorbed energy is of the order of eV, the excitation or inoisation of slightly bound electrons can be observed.
The bonds of electrons in teh inner shells of heavy atoms are of the order tens or hundereds of keV.
Therefore, the excitation or ionisation of electron from these shells may result in the emission of ultraviolet light or of X-rays.
In general, IR-light, visible or UV-light and also X-rays can be emitted by excited atoms, depending ont he difference between excited and basic energy levels.
