When we examine the spectral lines emitted by a hydrogen discharge tube, we notice that each line is not a single, sharp wavelength but rather spread over a small range of wavelengths. This phenomenon can be attributed to several factors, but the most likely explanation among the options provided is (a) the Doppler effect, as the gas atoms emitting light are in motion.
Understanding the Doppler Effect
The Doppler effect refers to the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source. In the context of a hydrogen discharge tube, the gas atoms are in constant motion, and as they emit light, their movement can cause shifts in the observed wavelengths.
How Motion Affects Wavelengths
- Redshift: If an atom is moving away from the observer, the emitted light waves are stretched, resulting in longer wavelengths (redshift).
- Blueshift: Conversely, if an atom is moving towards the observer, the emitted light waves are compressed, leading to shorter wavelengths (blueshift).
This motion of the atoms creates a range of wavelengths for each spectral line, as different atoms are moving at different velocities relative to the observer. Thus, the spectral lines appear broadened rather than sharp and distinct.
Other Factors Considered
While the Doppler effect is the most significant contributor to the broadening of spectral lines, let's briefly examine the other options:
Recoil of Atoms
Option (b) suggests that the recoil of an atom when it emits a photon could cause broadening. While this does occur, the effect is relatively minor compared to the Doppler effect, especially in a gas where atoms are not tightly bound.
Photon Collisions
Option (c) mentions collisions of photons with free electrons. While such interactions can occur, they typically do not lead to significant broadening of spectral lines in a discharge tube setting.
Energy Level Variations
Option (d) posits that the energy levels in excited atoms differ slightly from those predicted by Bohr's theory. While this is true to some extent due to various factors like fine structure and hyperfine splitting, it does not primarily account for the observed broadening of spectral lines in this context.
Conclusion
In summary, the broadening of spectral lines in a hydrogen discharge tube is predominantly due to the Doppler effect caused by the motion of gas atoms emitting light. This motion results in a range of wavelengths for each spectral line, leading to the observed spread rather than a sharp line. Understanding this concept is crucial for interpreting spectral data in various fields, including astrophysics and quantum mechanics.
