# Bohr Model Calculator

Hydrogen level n: r_n = n²a₀, E_n = −13.605693/n² eV, v_n = αc/n, orbital period, plus optional transition energies with named series lines.

> Canonical page: https://elysiatools.com/en/tools/bohr-model-calculator

- **Category:** Science & Education

- **Keywords:** bohr model, hydrogen atom, energy levels, bohr radius, rydberg, atomic transition, quantum mechanics

## Overview

The Bohr Model Calculator computes hydrogen atomic properties for any principal quantum number n, including orbital radius, energy level, electron orbital speed, and orbital period. It also calculates transition energy, photon emission or absorption wavelength, and identifies the corresponding spectral series when an optional target quantum level m is provided.

## Inputs

- **Principal quantum number n** (number): e.g. 2
- **Transition to level m (optional)** (number): e.g. 1

## When to use

- Determining physical properties of hydrogen orbitals such as radius, orbital velocity, and orbital period for a given quantum level n.
- Calculating photon energy differences and emission or absorption wavelengths between two atomic states (n to m).
- Identifying named hydrogen spectral series (Lyman, Balmer, Paschen, Brackett, Pfund, Humphreys) and ionization thresholds.

## How it works

- Enter the initial principal quantum number n (from 1 to 1000) for the hydrogen electron state.
- Optionally enter a destination quantum level m to compute an atomic electron transition.
- View computed orbital parameters including radius (r_n), binding energy (E_n), orbital velocity (v_n), period (T), and transition wavelength (λ).

## Use cases

- Solving quantum mechanics and atomic physics homework problems on hydrogen orbital mechanics.
- Verifying experimental spectroscopy wavelengths against theoretical hydrogen emission lines.
- Evaluating orbital speed percentages relative to the speed of light across different quantum states.

## Frequently asked questions

### What formulas are used for single-level calculations?

The calculator evaluates orbital radius as r_n = n²a₀, energy as E_n = −13.605693/n² eV, velocity as v_n = αc/n, and orbital period as T = 2πr/v.

### How is transition photon wavelength calculated?

It computes the energy difference ΔE = |E_n − E_m| and converts it to photon wavelength via λ = hc/ΔE.

### What indicates photon emission versus photon absorption?

A transition to a lower state (m < n) emits a photon, while a transition to a higher state (m > n) absorbs a photon.

### Which spectral series does the tool recognize?

Transitions are categorized based on lower level m: Lyman (m=1), Balmer (m=2), Paschen (m=3), Brackett (m=4), Pfund (m=5), and Humphreys (m=6).

### Can this calculator evaluate hydrogen-like ions with Z > 1?

No, calculations use standard physical constants specific to the neutral hydrogen atom with atomic number Z = 1.

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