Question

Explain Bohr's model of the atom.

Hint:

Bohr’s model introduced the concept of quantized energy levels, which helped explain the discrete spectral lines observed in atomic spectra.

Answer 1

Bohr's model of the atom was proposed by Niels Bohr in 1913 to explain the structure of the hydrogen atom and the discrete energy levels of electrons. According to Bohr's model:
1. **Electron Orbitals:** Electrons revolve around the nucleus in fixed, circular orbits without radiating energy. These orbits are called "stationary orbits" or "energy levels."
2. **Quantized Energy Levels:** The energy associated with each orbit is quantized, meaning that only certain energy levels are allowed. The energy of an electron in the \( n \)-th orbit is given by:
\[ E_n = - \frac{13.6 \, \text{eV}}{n^2} \] where \( n \) is the principal quantum number (1, 2, 3, ...).
3. **Electron Transitions:** Electrons can absorb or emit energy in discrete amounts when they jump between these orbits. The energy of the emitted or absorbed radiation is equal to the difference in energy between the two orbits:
\[ \Delta E = E_{\text{higher}} - E_{\text{lower}} \] 4. **Angular Momentum Quantization:** The angular momentum of an electron in the \( n \)-th orbit is quantized and is an integer multiple of \( \hbar = \frac{h}{2\pi} \) (where \( h \) is Planck’s constant):
\[ L = n \hbar \] Bohr's model successfully explained the spectral lines of hydrogen and laid the foundation for quantum mechanics.