# Determine the wavelenghts of photons

• soul5
In summary, wavelength is the distance between two consecutive peaks or troughs of a wave. The wavelengths of photons can be measured using a spectrophotometer, and it is important to determine them in order to understand the properties and behavior of light. Common units for measuring wavelengths include nanometers and angstroms. The wavelengths of photons can be changed through processes such as diffraction, refraction, and absorption, as well as by altering the energy level of the associated atom or molecule.
soul5

## Homework Statement

Determine the wavelenghts of photons given off for the 3rd line in the Lyman series, the 2nd line in the Balmer series and the 1st line in the Paschen series.

## The Attempt at a Solution

Lyman series: n=1
Balmer series: n=2
Paschen Series: n=3

What do I do?

If you look up the Bohr Model you should come across the equation(s) you need to solve this. See if you can find it.

To determine the wavelengths of photons for these series, we can use the Rydberg formula. This formula relates the wavelengths of photons emitted by hydrogen atoms to their energy levels. It is given by:

1/λ = R (1/n1^2 - 1/n2^2)

Where λ is the wavelength, R is the Rydberg constant (1.097x10^7 m^-1), and n1 and n2 are the energy levels of the electron.

For the Lyman series, n1=1 and n2=∞ (since the electron is transitioning from the highest energy level to n=1). Plugging these values into the formula, we get:

1/λ = R (1/1^2 - 1/∞^2)

1/λ = R (1 - 0)

1/λ = R

λ = 1/R = 91.2 nm

Therefore, the wavelength of photons emitted in the 3rd line of the Lyman series is 91.2 nm.

Similarly, for the Balmer series, n1=2 and n2=∞, so the formula becomes:

1/λ = R (1/2^2 - 1/∞^2)

1/λ = R (1/4 - 0)

1/λ = R/4

λ = 4/R = 364.8 nm

And for the Paschen series, n1=3 and n2=∞, giving us:

1/λ = R (1/3^2 - 1/∞^2)

1/λ = R (1/9 - 0)

1/λ = R/9

λ = 9/R = 1094.4 nm

In summary, the wavelengths of photons emitted in the 3rd line of the Lyman series, the 2nd line of the Balmer series, and the 1st line of the Paschen series are 91.2 nm, 364.8 nm, and 1094.4 nm, respectively.

## What is the definition of wavelength?

Wavelength is the distance between two consecutive peaks or troughs of a wave.

## How are wavelengths of photons measured?

The wavelengths of photons can be measured using a spectrophotometer, which separates the light into different wavelengths and measures their intensity.

## Why is it important to determine the wavelengths of photons?

Determining the wavelengths of photons is important because it helps us understand the properties and behavior of light. It is also crucial in fields such as astronomy, where the study of different wavelengths of light can reveal information about distant objects in the universe.

## What are some common units for measuring wavelengths?

The most common units for measuring wavelengths of photons are nanometers (nm) and angstroms (Å). Both units are used to represent very small distances, with 1 nm equaling 0.000000001 meters and 1 Å equaling 0.0000000001 meters.

## Can the wavelengths of photons be changed?

Yes, the wavelengths of photons can be changed through different processes such as diffraction, refraction, and absorption. In addition, the wavelength of a photon can also be altered by changing the energy level of the atom or molecule that it is associated with.

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