Write down the postulates of Bohr's model for the hydrogen atom.

(N/A) $(i)$ Principal quantum number: The stationary states for the electron are numbered $n = 1, 2, 3, \dots$. These integral numbers are known as Principal quantum numbers.
(ii) Stationary orbit radii $(r)$: The radii of the stationary states are expressed as: $r_n = n^2 a_0$, where $a_0 = 52.9 \text{ pm}$.
- The radius of the first stationary $(n = 1)$ state, called the Bohr orbit, is $52.9 \text{ pm}$.
- Normally, the electron in the hydrogen atom is found in this orbit $(n = 1)$.
- As $n$ increases, the value of $r$ increases, meaning the electron is present further away from the nucleus.
(iii) Energy of stationary state: The energy of the stationary state is given by the expression: $E_n = -R_H \left(\frac{1}{n^2}\right)$, where $n = 1, 2, 3, \dots$ and $R_H$ (Rydberg constant) $= 2.18 \times 10^{-18} \text{ J}$.
- The energy of the ground state $(n = 1)$ is $E_1 = -2.18 \times 10^{-18} \text{ J}$.
- The energy of the stationary state for $n = 2$ is $E_2 = -2.18 \times 10^{-18} \text{ J} \times \left(\frac{1}{2^2}\right) = -0.545 \times 10^{-18} \text{ J}$.
- When the electron is free from the influence of the nucleus, the energy is taken as zero $(n = \infty)$, which corresponds to an ionized hydrogen atom $(H^+)$.