Calculate Wavelength and Frequency N 4 N 3

This calculator computes the wavelength and frequency of the n=4 to n=3 transition in hydrogen using the Rydberg formula. The results are displayed in meters and Hertz, with a visualization of the energy levels.

Introduction

The n=4 to n=3 transition in hydrogen is a spectral line in the red part of the visible spectrum. This transition occurs when an electron drops from the fourth energy level to the third energy level in a hydrogen atom.

The wavelength and frequency of this transition can be calculated using the Rydberg formula, which relates the wavelength of light to the difference in energy levels of the electron.

Formula

The Rydberg formula for the wavelength of light emitted when an electron transitions from level n₂ to n₁ is:

λ = R × (1/n₁² - 1/n₂²)^-1

Where:

λ = wavelength (in meters)
R = Rydberg constant (1.0973731568160 × 10⁷ m^-1)
n₁ = lower energy level (3 for n=4 to n=3 transition)
n₂ = higher energy level (4 for n=4 to n=3 transition)

The frequency (ν) can be calculated from the wavelength using the speed of light (c):

ν = c / λ

Where:

ν = frequency (in Hertz)
c = speed of light (2.99792458 × 10⁸ m/s)

Calculation

For the n=4 to n=3 transition in hydrogen:

Identify the energy levels: n₁ = 3, n₂ = 4
Calculate the wavelength using the Rydberg formula
Calculate the frequency using the wavelength and speed of light

Note: The Rydberg constant and speed of light values used are the currently accepted values from the CODATA database.

Example

Let's calculate the wavelength and frequency for the n=4 to n=3 transition:

Using the Rydberg formula:

λ = 1.0973731568160 × 10⁷ × (1/3² - 1/4²)^-1

λ = 1.0973731568160 × 10⁷ × (1/9 - 1/16)^-1

λ = 1.0973731568160 × 10⁷ × (0.1111... - 0.0625)^-1

λ = 1.0973731568160 × 10⁷ × (0.0486...)^-1

λ ≈ 2.121 × 10^-7 meters
Calculate the frequency:

ν = 2.99792458 × 10⁸ / 2.121 × 10^-7

ν ≈ 1.413 × 10¹⁵ Hertz

This calculation shows that the n=4 to n=3 transition emits light with a wavelength of approximately 212.1 nm and a frequency of approximately 1.413 × 10¹⁵ Hz.

FAQ

What is the n=4 to n=3 transition in hydrogen?: The n=4 to n=3 transition is a spectral line in the red part of the visible spectrum that occurs when an electron drops from the fourth energy level to the third energy level in a hydrogen atom.
What is the Rydberg formula?: The Rydberg formula is an empirical formula that relates the wavelength of light to the difference in energy levels of the electron in a hydrogen atom.
What units are used for wavelength and frequency?: The wavelength is measured in meters, and the frequency is measured in Hertz.
What is the speed of light used in the calculation?: The speed of light used is the currently accepted value from the CODATA database: 2.99792458 × 10⁸ m/s.
What is the Rydberg constant used in the calculation?: The Rydberg constant used is the currently accepted value from the CODATA database: 1.0973731568160 × 10⁷ m^-1.