Question

Explain the Balmer and Rydberg equations.

Answer 1

Balmer's theory:

1. Balmer introduced a series to relate the wavelength of spectral lines with the energy shells having different energy levels. ( energy levels having $n=3,4,5...$so on)
2. This series is known as the Balmer series. This gives the wavelength of these lines.
3. Mathematically:

$\frac{1}{\lambda }=R\left[\frac{1}{2^2}-\frac{1}{n^2}\right]$

where $n$ are integers, $3,4,5,...$up to infinity, $\lambda$= wavelength and $R$ is a constant now called the Rydberg constant.

In the S.I. system of units, $R=1.097x{10}^7{m}^{-1}$

By the above equation,we can see that wavelength$\left(\lambda \right)$$\propto \frac{1}{n}$

Balmer's Observations:

1. When an electron jumps from any vertical orbit to a second vertical line, the emitted spectral lines are said to fall into the Balmer Series.
2. It is a series of lines in an electric spectrum lying on the surface.
3. Rydberg also introduced a standard formula for this to make it possible to calculate the wavelength of any line in the spectrum of hydrogen emission.

Rydberg's theory:

1. Rydberg's theory is based on the calculations of light wavelengths.
2. When an electron changes from a high-energy orbit to another of lower energy, then the electron energy changes, and a photon of light is created.
3. Mathematically

$\frac{1}{\lambda }=R{Z}^2\left[\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2}\right]$

Where $\lambda$=wave length of the photon, $Z$ = Atomic number of the atom, $n_1\&n_2$ are integers where $n_2>n_1$

Rydberg's Observations:

1. It turns out that there are spectra families that follow the Rydberg pattern.
2. Especially in alkaline metals, sodium, potassium, etc., but not with precision, hydrogen atomic lines follow the Balmer series.

Both the Balmer and Rydberg equations are used to represent the wavelength of a series of hydrogen spectrum lines.