Question

can you please discuss how hydrogen emission spectrum and energy level experiment proves that light emitted from excited hydrogen atom is quantized? also discuss any possible sources of error and ways to minimize these errors.
thanks:)

Answer 1

When the hydrogen atoms absorb energy, the electrons in them can jump to higher energy levels or get completely knocked out if the energy of the photon matches that of the energy of the electron. In both cases, the atom becomes unstable and eventually, electrons return back to their ground states by losing the same energies that were absorbed by them when they jumped to higher energy levels (including getting knocked out). The energy loss is in the form of electromagnetic radiation and can be captured on a screen by passing through a prism. A pattern containing a series of different wavelengths is obtained and is commonly referred to as 'emission spectrum' as against 'absorption spectrum' which studies the remaining wavelengths of the incident light. Both these spectrums are inverse of each other.

The emission spectrum of hydrogen has two important features listed below:

1) The energy emitted is not continuous but in the form of lines of discrete wavelengths.

2) The wavelengths of lines can be calculated by Balmer's formula.

1/$\lambda$ = R_H (1/n₁² - 1/n₂²), where R_H is Rydberg's constant having the value 109677 cm^-1

The presence of discrete lines and not continuous spectrum suggests that electrons in an atom cannot have just any energy but only certain discrete values that are seen as lines in emission and absorption spectra. This finding led Neil Bohr to formulate the concept of energy levels. Further, the energies associated with the lines in the emission spectrum of hydrogen are equal to the energies of photons that were absorbed by the electrons. The energy associated with the photon and hence electron is given by Plank's quantum theory and the following formula:

E = h$\nu$; where h is Plank's constant and $\nu$ is the frequency associated with the spectral line.

Hence, the energy emitted in the form of light in the hydrogen spectrum is quantized.

Sources of error in the hydrogen emission spectrum experiment

1) Calibration of the procedure to note down wavelengths of spectral lines.

2) The tube containing the hydrogen gas must have very low pressure as high pressure would make resistance high and collisions frequent due to which chemical reactions may occur.

To minimize the error in calibration, the spectrum of known elements (e.g. mercury) must be used before the experiment to calibrate the apparatus and sufficiently low pressure must be created in the tube containing hydrogen and then high voltage should be applied.