Rydberg Equation Calculator

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 = RZ²(1/n_i²−1/n_f²). 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*10⁷ 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.

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(ni)	Final state(nf)	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

• 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.

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 = RZ²(1/n_f² − 1/n_i²)

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

1/λ = 1.0947×10⁷(1/3²−1/4²)

1/λ = 1.0947×10⁷(7/144)

1/λ = 0.0532×10⁷

1/λ = 18.74731483771856×10⁷

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

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 = RZ²(1/n_f² − 1/n_i²)

We can change the Rydberg Equation as z = √1 /(R * λ* ((1/n_f²−1/n_i²))

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