In 1913, Niels Bohr solved the problem that electron orbits didn't follow classical physics. So he postulated that for a hydrogen atom:
- The electron moves in circular orbits around the nucleus with the motion described by classical physics
- The electron has only a fixed set of allowed orbits. These possible orbits have these possible values nh/(2pi), where n must be an integer (h is Planck's constant)
- An electron can pass from one allowed orbit to another when energy is absorbed or emitted
The allowed states for an electron are numbered: n = 1, 2, 3, 4, ... These integral numbers, which arise from point 2, are called quantum numbers.
The Bohr Theory predicts the radii of the allowed orbits
rn = n2a0, where n = 1,2,3... and a0 = 53 pm
When a free electron is attracted to the nucleus and confined to the orbit n, the electron energy can be described with this equation.
En = -RH/n2
RH is a constant that equals 2.179 * 10^-18 J
Is it likely that there is an energy level for the hydrogen atom, En = -100 * 10-20 J?
In order to prove that the answer is no, we have to show that n wouldn't be an integer.
n2 = -RH/n2
= -2.179 * 10-18 J/ -1.00 * 10-20 J
= 2.179 x 102 = 217.9
n = sqrt(217.9) = 14.76
14.76 isn't an integer, so it's NOT an allowed energy level.
Normally, the electron in a hydrogen atom is found in the orbit closest to the nucleus (n = 1). This is the lowest energy, or the ground state. When the electron gains a quantum of energy, it moves to a higher level (n = 2, 3, and so on) and the atom is in an excited state. When a electron moves from a higher to a lower numbered orbit, a unique quantity of energy is emitted- the difference between the two levels.
change in Energy = Ef - Ei = -RH/nf2 - -RH/ni2 = RH(1/ni2 - 1/nf2)
= 2.179 * 10-18 J(1/ni2 - 1/nf2)