Transition From N 5 to N 3 Calculate Wavelength

Introduction

The transition of an electron between energy levels in a hydrogen atom results in the emission or absorption of electromagnetic radiation. The wavelength of this radiation can be calculated using the Rydberg formula, which relates the wavelength to the initial and final energy levels of the electron.

In this case, we're calculating the wavelength emitted when an electron drops from the n=5 level to the n=3 level in a hydrogen atom.

Formula

The wavelength (λ) of the emitted photon can be calculated using the Rydberg formula:

Where:

• λ is the wavelength in meters
• R is the Rydberg constant (1.0973731568508 × 10⁷ m⁻¹)
• n₁ is the initial energy level (5 in this case)
• n₂ is the final energy level (3 in this case)

The result will be in meters, which can be converted to nanometers by multiplying by 10⁹.

Calculation

Using the Rydberg formula with n₁ = 5 and n₂ = 3:

Since wavelength cannot be negative, we take the absolute value: 1.287 × 10⁻⁷ m or 128.7 nm.

This calculation shows the wavelength of light emitted when an electron transitions from n=5 to n=3 in a hydrogen atom.

Example

Let's say you're studying the emission spectrum of hydrogen and want to verify the wavelength for the transition from n=5 to n=3. Using our calculator:

1. Enter initial level (n₁): 5
2. Enter final level (n₂): 3
3. Click "Calculate"

The calculator will display the wavelength as approximately 128.7 nm, which matches our manual calculation.

This example demonstrates how the calculator can be used to verify theoretical predictions about atomic transitions.