Question

Write the postulates of Bohr’s atomic model. What is the relationship between the radii of the nth and first Bohr orbit of a hydrogen atom?

Answer 1

Hint: To determine the structure of an atom, various scientists proposed their atomic models. One such atomic model proposed by Neil Bohr was called Bohr's atomic model. This atomic model also determined the frequency of emitted radiation as well as the angular momentum of an electron.

Complete answer:
The postulates of Bohr’s atomic model are:
-Atoms consist of a nucleus in the centre around which the electrons are revolving in circular fixed paths called as orbits (shells, energy levels, stationary states).
- The energy of an electron is constant means when the electron is revolving in an orbit its energy does not change with time, so Bohr’s orbits are called stationary orbits.
- The energy of an electron is changed when it moves from one energy level to another. It absorbs energy from lower orbit to higher and emits energy from higher to lower orbit.
- The frequency of radiation emitted is directly proportional to the change in energy. This means $\Delta E={{E}_{2}}-{{E}_{1}}$ where $E=h\nu $.
- The angular momentum of an electron is an integral multiple of $\dfrac{h}{2\pi }$ . This gives the angular momentum of an electron in an orbit as $mvr=\dfrac{nh}{2\pi }$.
The relationship between the nth and the first Bohr orbit of hydrogen atom is ${{r}_{n}}={{r}_{1}}\times {{n}^{2}}$ , where n is the energy level and r is the radius in various orbits.

Note:
The radius of stationary state is given by the expression $r=0.529\dfrac{{{n}^{2}}}{Z}$, where n is the energy level, Z is the atomic number of the atom. So, for hydrogen atoms in the first stationary state the radius is r = 0.0529 nm (nanometer). This formula of radius is applicable for the hydrogen-like species, meant for lighter atoms.