Question

Can someone explain to me Bohr's model of hydrogen and Bohr Selection Rule

Answer 1

Bohr’s model of the hydrogen atom started from the planetary model, but he added one assumption regarding the electrons. What if the electronic structure of the atom was quantized? Bohr suggested that perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius. Only shells with a radius given by the equation below would be allowed, and the electron could not exist in between these shells. Mathematically, we could write the allowed values of the atomic radius as r(n)=n^2 * r(1),

where n is a positive integer, and r(1) is the Bohr radius, the smallest allowed radius for hydrogen.

He found that Bohr radius = r(1) = 0.529*10^-10 m

By keeping the electrons in circular, quantized orbits around the positively-charged nucleus, Bohr was able to calculate the energy of an electron in the nth energy level of hydrogen:

E(n) = -13.6/n^2 eV

where the lowest possible energy or ground state energy of a hydrogen electron E(!) = -13.6 eV

Note that the energy is always going to be a negative number, and the ground state, n=1 has the most negative value. This is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus, n = infinity which is defined to have an energy of 0 eV. Since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus, the energy of an electron in orbit is always negative.

According to Bohr's selection rule, there can only be quantum jumps between stationary states that are one or three stationary states apart. So, for example, there can be transitions from the n = 100 stationary state to the n = 99 or n = 97 stationary states; but there cannot be transitions from the n = 100 stationary state to the n = 98 stationary state, because there is no second harmonic in the classical electron orbit.