Question

What are the Bohr's Postulates for the hydrogen atom? Write down the following for electrons in the ground state of hydrogen atom:
(i) Binding energy
(ii) Angular momentum
(iii) Total energy

Hint:

Bohr's model explains discrete energy levels and quantization of angular momentum.

Answer 1

Bohr's Postulates for Hydrogen Atom:

• Electrons revolve in fixed orbits without emitting energy.
• Only certain discrete orbits are allowed where angular momentum is quantized.
• Electrons emit or absorb energy when transitioning between orbits.

Step 1: Binding Energy

\[ E_{\text{binding}} = 13.6 \, \text{eV} \]

\( E_{\text{binding}} = 13.6 \text{ eV} \)

Step 2: Angular Momentum

According to Bohr's quantization condition:

\[ m v r = n \hbar \]

For ground state \( n = 1 \):

\[ L = \hbar = \frac{h}{2\pi} \]

\( L = \frac{h}{2\pi} \)

Step 3: Total Energy

Total energy of an electron in the ground state:

\[ E = -\frac{13.6}{n^2} \, \text{eV} \]

For \( n = 1 \):

\( E = -13.6 \text{ eV} \)