Calculate The Wavelength of The Following N 3 N 2

Introduction

In quantum physics, the wavelength of light emitted or absorbed during electronic transitions between energy levels can be calculated using the Rydberg formula. This calculator specifically handles the transition from n=3 to n=2.

The Rydberg formula is fundamental in atomic spectroscopy and helps scientists understand the energy levels of electrons in atoms. The wavelength calculation is crucial for identifying spectral lines in emission or absorption spectra.

Formula

The wavelength (λ) for the transition from n1 to n2 is calculated using the Rydberg formula:

The result is typically converted to nanometers (nm) by multiplying by 10^-9.

Worked Example

Let's calculate the wavelength for the n=3 to n=2 transition:

1. Identify the quantum numbers: n1 = 3, n2 = 2
2. Plug values into the formula:
   λ = 1 / (1.0973731568508 × 10⁷ (1/2² - 1/3²))
3. Calculate the difference inside the parentheses:
   1/4 - 1/9 = 0.25 - 0.1111 = 0.1389
4. Multiply by the Rydberg constant:
   1.0973731568508 × 10⁷ × 0.1389 ≈ 1.521 × 10⁶ m^-1
5. Take the reciprocal to get wavelength in meters:
   λ ≈ 1 / 1.521 × 10⁶ ≈ 6.57 × 10^-7 m
6. Convert to nanometers:
   6.57 × 10^-7 m × 10⁹ nm/m ≈ 657 nm

The calculated wavelength for the n=3 to n=2 transition is approximately 657 nanometers.

Interpreting Results

The wavelength you calculate represents the specific electromagnetic radiation emitted when an electron transitions from the n=3 to n=2 energy level in a hydrogen atom. This wavelength corresponds to a particular color in the visible spectrum.

For the n=3 to n=2 transition, you should expect a wavelength around 657 nm, which falls in the red part of the visible spectrum. This is known as the red hydrogen-alpha line.