# Rydberg Equation Calculator

You can calculate wavelength and atomic number by using the Rydberg Equation calculator. Simply, enter the atomic number and primary quantum numbers of the initial and final states of an emitted light in the tool and click on the calculate button to avail the output in seconds.

### Rydberg Equation Formula

The Rydberg formula is a mathematical method of estimating light wavelength. When an electron moves from one atomic orbit to another, the energy of the electron shifts. The photon of light is formed when an electron moves from a high-energy orbit to a lower-energy orbit. The photon of light is also absorbed by the atom as the electron shifts from a low to a higher energy state.

The calculator uses the formula to determine the wavelength of an emitted light.

**1/λ = RZ ^{2}(1/n_{i}^{2}−1/n_{f}^{2})**. Since,

**n**

_{f}>n_{i}- Where, λ is the wavelength of emitted light in vacuum
- R
_{H}be the Rydberg constant for hydrogen whose value is approximately (1.097*10^{7}m^{-1}) - Z be the number of protons in the nucleus of the element
- n
_{f}be the principal quantum number in the final state - n
_{i}be the principal quantum number in the initial state

For more concepts check out physicscalculatorpro.com to get quick answers by using this free tool.

### Hydrogen Emission Spectrum

You can understand about the many spectral line series found in hydrogen, as well as an approach that utilises the emission spectrum by referring to the below mentioned table.

Initial state(n_{i}) |
Final state(n_{f}) |
Series |
---|---|---|

1 | n ≥ 2 | Lyman series |

2 | n ≥ 3 | Balmer series |

3 | n ≥ 4 | Paschen series |

4 | n ≥ 5 | Brackett series |

5 | n ≥ 6 | Pfund series |

6 | n ≥ 7 | Humphreys series |

### How do you use Rydberg Equation to find Wavelength?

- Determine the number of protons in the element's nucleus first. Either hydrogen or a hydrogen-like element will be required.
- Establish the element's primary quantum numbers.This will be the element's initial and final numbers after it has undergone an energy level change.
- Finally, we can get the light's wavelength to calculate the wavelength of the light emitted as a result of the element's energy levels changing.

### Rydberg Equation Examples

**Question 1:** Find the wavelength of an electron's electromagnetic radiation as it relaxes from n = 4 to n = 1?

**Solution:**

Consider the problem, we have

Initial stage, n_{i} = 3

Final stage, n_{f} = 4

We know that, Rydberg’s constant, RH is approximately 1.9074 ×107m^{-1}.

The Rydberg equation:**1/λ = RZ ^{2}(1/n_{f}^{2} − 1/n_{i}^{2})**

Substituting the inputs, we get the following equation for Wavelength of Rydberg Equation:

1/λ = 1.0947×10^{7}(1/3^{2}−1/4^{2})

1/λ = 1.0947×10^{7}(7/144)

1/λ = 0.0532×10^{7}

1/λ = 18.74731483771856×10^{7}

Therefore, The wavelength in meters the value of Rydberg’s constant is λ= 1.875×10^{−6}meter.

**Question 2:** Find the atomic number for hydrogen if the wavelength of an electron radiation is 150m with the energy level from n = 2 to n = 1?

**Solution:**

Consider the problem, we have

Wavelength, λ = 150m

Initial state, n_{i} = 2

Final state, n_{f} = 1

We know that: The Rydberg’s constant, RH is approximately 1.9074 ×107m^{-1}.

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

By using the Rydberg equation: **1/λ = RZ ^{2}(1/n_{f}^{2} − 1/n_{i}^{2})**

We can change the Rydberg Equation as z = √1 /(R * λ* ((1/n_{f}^{2}−1/n_{i}^{2}))

Substitute the values into the equation, we get

Atomic number, Z = √1 /(R *150 * (1/1² - 1/2²))

Atomic number, Z = 284.61713926861565*10^{-07}

Therefore, Atomic number, Z = 2.846*10^{-05}

### FAQs on Rydberg Equation Calculator

**1. What is the formula for calculating the Rydberg Equation Wavelength?**

The formula to determine the wavelength of an emitted light that is emitted when hydrogen-like elements are switching to different energy levels is **1/λ = RZ ^{2}(1/n_{i}^{2} − 1/n_{f}^{2})**.Since, n

_{f}>n

_{i}.

**2. What is n _{1} and n_{2} in Rydberg Equation?**

n_{1} and n_{2} are integers in Rydberg Equation.

**3. What is the hydrogen spectrum formula?**

The following formula can be used to compute the observed hydrogen-spectrum wavelengths: 1/λ=R(1/n_{i}^{2}−1/n_{f}^{2}).Since, The atomic number of hydrogen is Z = 1