The
Open Door Web Site |
||||||||||||||||||||||||||||||||||||||||
|
Atomic and Nuclear Physics The Bohr Model of the Atom Bohr proposed that the “quantum” of
angular momentum, L, possessed by the electron in a hydrogen
atom is h/(2 Therefore, the “angular momentum levels” are given by
where n is an integer. So, in the
lowest level L = h/2
Angular momentum, L = mvr
The force acting on the electron is given by
If the electron orbits in a circular path, the force is also equal to
so, the speed, v, of the electron is given by
Substituting this into equation 1 allows us to calculate the radii of the allowed orbits
The K.E. of the electron ½mv2 which gives
The potential, V, at a point a distance r away from a proton is given by
Therefore the potential energy possessed by an electron at a distance r away from a proton is given by
The total energy (K.E. + P.E.) is therefore
Substituting for r from equation 2, we have
We see that
En is proportional to 1/n2
where the constant of proportionality is
If an electron falls from one energy level, ninitial to a lower level, nfinal, then the energy of the quantum of electro-magnetic radiation emitted is equal to the difference between the two levels and is therefore given by
which has the same form as the Balmer series if we put nfinal = 2
Put a close window in here |
|
||||||||||||||||||||||||||||||||||||||