# Rydberg Formula

## Rydberg Formula

The wavelength of light generated by an electron travelling between atomic energy levels is predicted by the Rydberg formula. Every element has its spectral fingerprint. Light is created when an element in its gaseous form is heated. Bright lines of various colours can be seen when this light travels through a prism or a diffraction grating. Each element stands out in some way from the others. With this finding, spectroscopic research commenced. This Extramarks article will go through the Rydberg formula in detail.

Each element has its unique spectral fingerprint. When an element in its gaseous form is heated, it emits light. When this light goes through a prism, brilliant lines of various colours may be seen. Each constituent differs somewhat from the others. This finding marked the beginning of spectroscopic research.

Johannes Rydberg was a Swedish scientist who discovered the mathematical link between one element’s spectral lines and the next. He noticed that the wave numbers of successive lines had an integer connection. The Rydberg Formula was created by combining his observations with Bohr’s concept of the atom.

The Rydberg Formula is written as is used to compute the spectra of different elements.

Ν¯=1/λ = R(1/n12 – 1/n22)

n1 and n2 are integers (n1 < n2),

λ = Wavelength of photon,

R = Rydberg constant [1.0973731568539(55) × 107 m-1].

In most circumstances, They will be dealing with hydrogen, which permits us to use the Rydberg Formula.

v¯ = 1/λ = RH(1/n12 – 1/n22)

n1 and n2 are integers (n1 < n2),

λ = Wavelength of the photon,

RH = Rydberg constant due to hydrogen [1.0973731568539(55) × 107 m-1].

The Rydberg formula is a mathematical formula used to calculate the wavelength of light emitted by an electron travelling between an atom’s energy levels. The energy of an electron changes as it moves from one atomic orbital to the next. An electron goes from a high-energy orbital to a lower-energy orbital, resulting in the production of a photon of light. Atoms absorb photons of light when an electron changes from a low-energy to a higher-energy state. The Rydberg Formula may be used to calculate the spectra of different elements.

## Derivation of Rydberg Formula

When an electron transitions from one orbit to another

ΔE = Ef – Ei

Where,

ΔE = Energy Difference,

Ef = Final Energy,

Ei = Initial Energy.

By using Bohr’s Model,

ΔE = (-RH/nf2) – (-RH/ni2)

∴ ΔE = RH/ni2 – RH/nf2

∴ ΔE = RH(1/ni2 – 1/nf2)

∴ ΔE = 2.18 × 10-18(1/ni2 – 1/nf2) ⇢ (Equation 1)

E = h{v}

Put the value of E in equation 1, and they get

∴ hv = 2.18 × 10-18(1/ni2 – 1/nf2)

v = 2.18 × 10-18/h × (1/ni2 – 1/nf2) ⇢ (Where h = 6.626 × 10-34)

v = 3.29 × 1015(1/ni2 – 1/nf2) ⇢ (Equation 1)

they have, c = λ{v}

1/λ = v/c

Divide equation 2 by c,

v/c = 3.29 × 1015/c × (1/ni2 – 1/nf2)

v¯ = 1/λ = 1.0974 × 107(1/ni2 – 1/nf2) m-1

## Solved Example

1. Why did Rydberg limit his tests to hydrogen?

Because it is an empirical formula based on the Bohr model of the hydrogen atom, the Rydberg equation can only be used for hydrogen and other hydrogenic molecules. The Rydberg constant is used to compute the wavelengths in the hydrogen spectrum, which represent the amount of energy absorbed or emitted as photons when electrons move between shells in the hydrogen atom.

2. What does the Rydberg Formula constant represent?

Because of its connection to the fundamental atomic constants (e, h, me, and c) and the precision with which it can be determined, the Rydberg Formula constant is one of the most significant constants in atomic physics. The Rydberg Formula constant was first published in the scientific literature in 1890. The Rydberg Formula constant is used to compute the wavelengths in the hydrogen spectrum, which represent the amount of energy absorbed or emitted as photons when electrons move between shells in the hydrogen atom.

In other words, the Rydberg Formula is a mathematical equation that predicts the wavelength of light generated by an electron transitioning between energy levels in an atom. The energy of an electron changes as it moves from one atomic orbital to the next.

3. Why are chemical formulas important?

The chemical formula is essential for comprehending several scientific concepts. Chemistry is about learning about chemical elements and compounds and how they interact to generate difficult-to-understand chemical equations. A chemical formula depicts the symbols of the elements in the compound as well as the elemental ratios.

To get high grades in chemistry, students must know the chemical formula. These formulae will assist them in passing their school examinations, board exams, and competitive tests. Simply learning the basic rules and element names will allow students to write chemical formulas on their own.