# Wavelengths and Balmer series

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In summary, the Balmer series, which is visible light, begins with a wavelength of 400 nm. To determine how many spectral lines have a wavelength greater than 400 nm, one can either count them in a book or online, or use the formula 1/lambda= R(1/2^2-1/n^2) with different values of n. While the series theoretically goes on forever with n=2 to infinity, after calculating a few wavelengths it becomes clear that only a few values of n are needed to answer the question. Additionally, increasing n results in a decrease in wavelength.

## Homework Statement

In the Balmer series, how many spectral lines have the wavelength greater than 400 nm?

## Homework Equations

1/lambda= R(1/2^2-1/n^2)
lambda=wavelength
r=rhydberg constant 1.097x10^7
n= 3,4,5...
balmer series is visible light

## The Attempt at a Solution

ok so i know the balmer series starts with 400 nanometers because its visible light, but i don't understand how to see how many spectral lines have wavelength greater.

You could just look up the Balmer Series in a book or on the web and count them.
Or use the formula to calculate the wavelengths - put in n=3, calculate. Put in n=4, calculate. Pretty soon you will have all the wavelengths you need!

ok. but when i do the calculating up to what number do i go? because i thought it went from 2 on.

Yes, it does go on forever - 2 to infinity. But after calculating 2 or 3 wavelengths, you will see that you don't have to do very many of them the answer your question.

o ok i got it. wavelength decreases when you increase n

## 1. What are wavelengths?

Wavelengths are the distance between two consecutive peaks or troughs in a wave. In the context of light, wavelengths refer to the distance between two consecutive crests or troughs in an electromagnetic wave.

## 2. What is the Balmer series?

The Balmer series is a series of spectral lines in the visible region of the electromagnetic spectrum that are emitted by excited hydrogen atoms when they return to their ground state. The series was named after Swiss physicist Johann Balmer, who first discovered the relationship between the spectral lines and the energy levels of hydrogen atoms.

## 3. What is the significance of the Balmer series?

The Balmer series is significant because it provided early evidence for the quantization of energy levels in atoms and laid the foundation for the development of the Bohr model of the atom. It also helped scientists understand the behavior of electrons and the emission of light from excited atoms.

## 4. What is the formula for calculating the wavelengths in the Balmer series?

The formula for calculating the wavelengths in the Balmer series is λ = 364.6(1/n2 - 1/4), where λ is the wavelength in nanometers and n is the principal quantum number.

## 5. How is the Balmer series related to other series in the hydrogen spectrum?

The Balmer series is just one of several series in the hydrogen spectrum. It is the only series in the visible region, while the other series, such as the Lyman series and the Paschen series, fall in the ultraviolet and infrared regions, respectively. These series all represent the transitions of electrons between different energy levels in hydrogen atoms.