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Calculate Wavelenth N 5 to N 1

Reviewed by Calculator Editorial Team

This calculator computes the wavelength of light emitted when a hydrogen atom transitions from the n=5 energy level to the n=1 ground state. The result is calculated using the Rydberg formula, which is fundamental in atomic physics.

Introduction

When an electron in a hydrogen atom moves from a higher energy level (n=5) to a lower one (n=1), it emits a photon with a specific wavelength. This transition is quantized and follows the Rydberg formula, which relates the wavelength to the energy levels involved.

The calculation is important in spectroscopy, quantum mechanics, and understanding atomic structure. The wavelength determines the color of light emitted, which can be used to identify elements in astrophysics.

Rydberg Formula

The wavelength (λ) of light emitted during a transition from level n2 to n1 in hydrogen is given by:

Formula

λ = R × (1/n12 - 1/n22)-1

Where:

  • R = Rydberg constant (1.0973731 × 107 m-1)
  • n1 = lower energy level (1 for ground state)
  • n2 = higher energy level (5 in this case)

The result is typically converted to nanometers (nm) for easier interpretation.

Calculation Process

The calculator follows these steps:

  1. Input the initial and final energy levels (n1 and n2)
  2. Apply the Rydberg formula to compute the wavelength in meters
  3. Convert the result to nanometers for readability
  4. Display the final wavelength with appropriate units

Assumptions

The calculation assumes a hydrogen atom in its ground state with no external influences. For other atoms or conditions, additional factors would need to be considered.

Worked Example

Let's calculate the wavelength for a transition from n=5 to n=1:

  1. R = 1.0973731 × 107 m-1
  2. n1 = 1, n2 = 5
  3. λ = (1.0973731 × 107) × (1/12 - 1/52)-1
  4. λ = (1.0973731 × 107) × (1 - 0.04)-1
  5. λ = (1.0973731 × 107) × 1.0416667
  6. λ ≈ 1.142 × 10-6 m
  7. Convert to nm: 1.142 × 10-6 m × 109 nm/m ≈ 1142 nm

The calculator should produce a similar result of approximately 1142 nm.

FAQ

What is the Rydberg constant?

The Rydberg constant (R) is a fundamental physical constant that relates to the wavelengths of spectral lines of many chemical elements. It has a value of approximately 1.0973731 × 107 m-1.

Why is the wavelength in the infrared range?

The calculated wavelength of 1142 nm falls in the infrared region of the electromagnetic spectrum, which is typical for transitions between higher energy levels in hydrogen atoms.

Can this be used for other atoms?

No, the Rydberg formula is specific to hydrogen. Other atoms have different energy level structures and require modified formulas.