Chapter 11, Problem 67A

Interpretation Introduction

Interpretation: This is to be proved that the energy levels of hydrogen atom are not continuous but quantized.

Concept introduction: According to Bohr’s atomic model limited numbers of orbits having certain energies are allowed or it can be said that the orbits are quantized.The electrons always revolve in stationary orbit,therefore, energy values of orbits are fixed and hence the changes in energies can have only certain values (somewhat similar to a staircase).

Answer to Problem 67A

The energy levels of hydrogen atoms are quantized.

Explanation of Solution

By observing the line spectrum of hydrogen,one can prove this fact.

When electricity is passed through a gas, light is emitted. When this light is passed through a prism only certain lines of light in the image is observed. This is called line spectra.

When a glass tube is filled with H₂ gas at low pressure and electric current is passed through it, the blue color is observed in the tube. When the blue light is passed through a prism, line spectrum is observed with few narrow lines rather than the continuous range of lines.

The hydrogen atomabsorbs or emits radiation of a certain frequenciesthus, these atoms can only absorb or emits radiation with certain energies. This is the reason of getting discrete colored lines corresponding to specific wavelength of transition of electrons from two different energy levels.

Conclusion

The energy levels of hydrogen atoms are quantized.