Rydberg Formula Calculator
⚛ Atomic & Quantum. Use the Rydberg formula (hydrogen-like) formula to find wavelength λ, atomic number z, lower level n₁, upper level n₂: pick the value you want, type the others, and the answer updates as you go.
With Z = 1 this is hydrogen: n₁ = 2, n₂ = 3 gives the red 656 nm line.
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Wavelength λ | nm |
| Atomic number Z | no unit |
| Lower level n₁ | no unit |
| Upper level n₂ | no unit |
Worked example
Find the wavelength λ when Atomic number Z = 1, Lower level n₁ = 2, Upper level n₂ = 3.
Using 1/λ = R_∞ Z²(1/n1² - 1/n2²): Wavelength λ = 656.11 nm.
Frequently asked questions
What is the formula for Rydberg formula (hydrogen-like)?
1/λ = R_∞ Z²(1/n1² - 1/n2²). With Z = 1 this is hydrogen: n₁ = 2, n₂ = 3 gives the red 656 nm line.
What do the letters stand for, and what units are used?
Wavelength λ in nm, Atomic number Z, Lower level n₁, Upper level n₂.
How do you calculate wavelength λ?
Put the values into 1/λ = R_∞ Z²(1/n1² - 1/n2²). For example, with Atomic number Z = 1, Lower level n₁ = 2, Upper level n₂ = 3, wavelength λ = 656.11 nm.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (wavelength λ, atomic number z, lower level n₁, upper level n₂) and fill in the others: it rearranges the formula for you.
