Wavelength of Light Emitted n=5 to n=4 Calculator

Calculator

Upper Level n_i

Lower Level n_f

Atomic Number Z

Rydberg Constant R, m^-1

Refractive Index

Speed of Light, m/s

Decimal Precision

Formula Used

The calculator uses the Rydberg equation for hydrogen-like atoms.

1 / λ = RZ²(1 / n_f² - 1 / n_i²)

λ_medium = λ_vacuum / refractive index

f = c / λ

E = hf

Here, λ is wavelength. R is the Rydberg constant. Z is atomic number. The upper level is n_i. The lower level is n_f.

How to Use This Calculator

Enter the upper quantum level. The default value is 5.
Enter the lower quantum level. The default value is 4.
Use Z = 1 for hydrogen.
Keep the default Rydberg constant unless your class uses another value.
Enter the refractive index. Use 1 for vacuum.
Press Calculate to see wavelength, frequency, and energy.
Use CSV or PDF buttons to save the result.

Example Data Table

Atom/Ion	Upper n	Lower n	Z	Approx. Wavelength	Region
Hydrogen	5	4	1	4050 nm	Infrared
Hydrogen	4	2	1	486 nm	Visible
Hydrogen-like helium	5	4	2	1012 nm	Infrared
Hydrogen	6	2	1	410 nm	Visible

Understanding the n=5 to n=4 Emission

Atoms emit light when an electron drops to a lower level. The lost energy becomes one photon. For hydrogen, a drop from n=5 to n=4 belongs to the Brackett series. It is called Brackett alpha. Its wavelength is near 4050 nm. That light sits in the infrared region. It is not visible to the human eye.

Why This Calculator Helps

The Rydberg equation gives a fast result. Still, small setup choices matter. A user may change the atomic number for hydrogen-like ions. They may adjust the Rydberg constant. They may also enter a refractive index. This page keeps those options clear. It reports wavelength in meters, nanometers, micrometers, and centimeters. It also returns frequency, photon energy, wave number, and spectral class.

Main Physics Idea

Energy levels are quantized. Only certain electron jumps are allowed. The jump size controls the photon energy. A larger drop gives a shorter wavelength. A smaller drop gives a longer wavelength. Because n=5 to n=4 is a small drop, the wavelength is long. The photon energy is also low compared with visible transitions.

Using Results Carefully

Vacuum wavelength is the standard reference value. Medium wavelength changes when refractive index is above one. The frequency stays linked to the emitted photon. Use nanometers for common spectra. Use micrometers for infrared reports. Use electron volts when comparing photon energy.

Useful Study Notes

The final level names the series. Final level one is Lyman. Final level two is Balmer. Final level three is Paschen. Final level four is Brackett. So n=5 to n=4 is the first Brackett line. In spectroscopy, this helps identify hydrogen in stars, gas clouds, and plasma lamps.

Practical Output

The calculator is useful for homework and lab checks. It shows each step in a compact way. You can compare vacuum wavelength with wavelength inside a medium. You can export the answer to CSV or PDF. The example table also helps test your own entries. Use the defaults for a quick hydrogen result. Then change values for related ions. Always keep the upper level larger than the lower level. Otherwise, the jump is absorption or invalid for emission. Record units, constants, and assumptions beside every final answer before submitting work.

FAQs

What is the wavelength for n=5 to n=4 in hydrogen?

It is about 4050 nm in vacuum. This equals about 4.05 micrometers. The value is in the infrared region.

Which spectral series contains this transition?

The transition ends at n=4, so it belongs to the Brackett series. The n=5 to n=4 line is Brackett alpha.

Is this emitted light visible?

No. The wavelength is much longer than visible red light. It lies in the infrared region, so normal human vision cannot see it.

Why must the upper level be larger?

Emission happens when an electron falls from higher energy to lower energy. If the upper level is not larger, the calculator cannot model emitted light.

What does atomic number Z do?

Z adjusts the equation for hydrogen-like ions. For normal hydrogen, use Z = 1. For singly ionized helium, use Z = 2.

Does refractive index change the result?

It changes wavelength inside a medium. A higher refractive index gives a shorter medium wavelength. Vacuum wavelength remains the standard reference.

What is photon energy?

Photon energy is the energy carried by one emitted photon. This calculator reports it in joules and electron volts.

Can I export my calculation?

Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable result file.