a) Describe the emission spectrum of a hydrogen discharge tube
b) Explain why different color lines appeared in different position in the spectrum. Use a suitable atomic model to help construct your answer.
c) Explain how do you decide if the lines observed are of the first order interference or from the higher order of interference.
a) The emission spectrum of a hydrogen discharge tube is a collection of distinct colored lines produced when an electric current is passed through a sealed tube containing hydrogen gas at low pressure. These lines correspond to different wavelengths or colors of light emitted by hydrogen atoms as they transition between different energy levels.
b) The appearance of different color lines in different positions in the spectrum can be explained using Bohr's atomic model. According to this model, an electron in a hydrogen atom can only occupy specific energy levels. When the electron absorbs energy, it moves to a higher energy level, and when it releases energy, it moves to a lower energy level. The energy levels in hydrogen are quantized, meaning they can only have certain specific values.
When an electric current is passed through the hydrogen discharge tube, the electrons in the hydrogen atoms gain energy and get excited to higher energy levels. As they return to lower energy levels, they release the excess energy in the form of light. Each transition from a higher to a lower energy level corresponds to a specific wavelength of light. The wavelength determines the color of light observed in the spectrum.
The different color lines observed in the spectrum correspond to different permitted energy level transitions in hydrogen. The Balmer series, for example, consists of visible light transitions where the electron moves from higher energy levels to the second energy level (n=2). Each line in the Balmer series corresponds to a specific transition and therefore has a distinct color. Other series, such as the Lyman and Paschen series, involve transitions to different energy levels and produce lines with different wavelengths and colors.
c) The interference pattern observed in a spectrum can provide clues about whether the lines are of the first order interference or from higher orders of interference. Interference occurs when waves interact with each other, resulting in constructive or destructive interference.
For first-order interference, the lines will be evenly spaced and exhibit a regular pattern. When light passes through a narrow slit or grating, it diffracts and creates multiple orders of interference. The first-order interference refers to the central maximum or the main peak in the pattern. The higher-order interferences correspond to additional peaks on either side of the central maximum. If the observed lines in the spectrum have a regular spacing between them, it suggests that they are of the first-order interference.
On the other hand, if the lines in the spectrum do not have a regular spacing and appear haphazard or irregular, it indicates that they may be originating from higher orders of interference. In higher orders, the peaks become closer together and may overlap, leading to a more chaotic pattern.
To determine the order of interference, one can compare the observed pattern with the expected pattern based on the properties of the diffraction grating or slit being used. By analyzing the spacing between the lines and their distribution, it is possible to differentiate between first-order and higher-order interferences.