### Rydberg Equation Calculator:

Our Rydberg equation calculator is a tool to help you calculate and understand the hydrogen emission spectrum.

Our calculator can also be used for other chemical elements, An atom with only one electron in them is called a hydrogen-like atom, e.g., if He⁺, Li²⁺ or Be³⁺. Read on to learn more about the series of different spectral lines found in hydrogen and the technique of using emission spectroscopy.

In the text below you will learn what the Rydberg formula is.

If you want to calculate the exact energy level of an atom like hydrogen, check out our hydrogen energy level calculator

### Rydberg Equation:

Rydberg equation one divided by 1/λ_{(m)} in meter is equal to the Rydberg constant for hydrogen R_{(m)} in meter and multiply the square of atomic number Z^{2} and multiply the one divided by the principal quantum number of the final state 1/ n_{2}^{2} and minus the one divided by the principal quantum number of the initial state 1/ n_{1}^{2}.Hence the Rydberg equation can be written as

1/λ_{(m)} = R_{(m)} *Z^{2} * ( 1/ n_{2}^{2} – 1/ n_{1}^{2})

Where

Λ = is the wavelength of emitted light

Z = is the atomic number (for hydrogen z =1 )

N_{1} = is the principal quantum number of the initial state (initial energy level)

N_{2} = is the principal quantum number of the final state (final energy level)

R = is the Rydberg constant for hydrogen R =1.0973 *10^{^}71/m

### Example:1

Calculate the atomic number 56 and initial state 42 and final state 15.Find the wavelength?

### Answer:

Atomic number =56

Initial state =42

Final state =15

Wavelength 1/λ = R *Z^{2} * ( 1/ n_{2}^{2} – 1/ n_{1}^{2})

Wavelength 1/ λ = 1.0973 *10^{^}71 *56.0^{2} (1/15^{2} – 1/ 42^{2} )

=1.3343*10^{71}m

Therefore wavelength 1.3343*10^{71 } m

### Example:2

Calculate the atomic number 48 and initial state 18 and final state 12.Find the wavelength?

### Answer:

Atomic number =48

Initial state =18

Final state =12

Wavelength 1/λ = R *Z^{2} * ( 1/ n_{2}^{2} – 1/ n_{1}^{2})

Wavelength 1/ λ = 1.0973 *10^{^}71 *48.0^{2} (1/12^{2} – 1/ 18^{2} )

=1.0252437*10^{-08 }m

Therefore wavelength 9.75377 *10^{71 }m