Physical chemistry LowerSixth
CHAPTER 5: BOHR’S MODEL FOR THE HYDROGEN ATOM
II. THE SPECTRAL LINES FOR ATOMIC HYDROGEN
- The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by ∆E, is given by :
Where E1 and E2 are the energies of the lower and higher allowed energy states respectively. This expression is commonly known as Bohr’s frequency rule.
- The angular momentum of an electron in a given stationary state can be expressed as in equation
Thus an electron can move only in those orbits for which its angular momentum is integral multiple of h/2π that is why only certain fixed orbits are allowed.
The details regarding the derivation of energies of the stationary states used by Bohr, are quite complicated and will be discussed in higher classes. However, according to Bohr’s theory for hydrogen atom:
a) The stationary states for electron are numbered n = 1,2,3.......... These integral numbers are known as Principal quantum numbers.
b) The radii of the stationary states are expressed as : rn =n2a0
Where a0 = 52, 9 pm. Thus the radius of the first stationary state, called the Bohr orbit, is 52.9 pm. normally the electron in the hydrogen atom is found in this orbit (that is n=1). As n increases the value of r will increase. In other words the electron will be present away from the nucleus.
C) The most important property associated with the electron, is the energy of its stationary state. It is given by the expression.
When the electron is free from the influence of nucleus, the energy is taken as zero. The electron in this situation is associated with the stationary state of Principal Quantum number = n = ∞ and is called as ionized hydrogen atom.
When the electron is attracted by the nucleus and is present in orbit n, the energy is emitted and its energy is lowered. That is the reason for the presence of negative sign in equation (2.13) and depicts its stability relative to the reference state of zero energy and n = ∞.
d) Bohr’s theory can also be applied to the ions containing only one electron, similar to that present in hydrogen atom. For example, He+ Li2+ , Be3+ and so on. The energies of the stationary states associated with these kinds of ions (also known as hydrogen like species) are given by the expression