Question

Explain how the Bohr model accounts for the four colored lines in the hydrogen line spectrum.

Short answer

The Bohr model accounts for the four colored lines in the hydrogen line spectrum as a result of electron transitions from higher energy levels (n=3, n=4, n=5, n=6) to the second energy level (n=2). Each transition releases a photon of light, the color of which is determined by the energy difference between the two states. The colors correspond to red, turquoise, blue, and violet.

Step-by-step solution

Brief of Bohr Model

The Bohr model was proposed by Niels Bohr in 1913. It explains that an atom is made up of a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus. These orbits are situated at distinct energy levels. Electrons can jump from one energy level to another.

Energy Level Transitions

When an electron in an atom jumps from a higher energy level to a lower energy level, it emits energy in the form of light. The energy difference between the two levels determines the wavelength (and hence color) of the light.

Relation to Hydrogen Line Spectrum

In a hydrogen atom, when the electron transitions from a higher energy state to a lower energy state (e.g., from n=3 to n=2 or n=4 to n=2), it emits a quantum of energy as a photon of light. The frequency (or color) of this light corresponds to the energy difference, and this is what we see as the hydrogen line spectrum.

Four Colored Lines

The four colored lines in the spectrum are due to the transitions of the electron to the second energy level from higher energy levels. The red color is due to the transition from the third energy level (n=3) to the second level (n=2). The turquoise line is due to a transition from the fourth level (n=4) to the second level (n=2). The blue line comes from the transition from the fifth level (n=5) to the second level, and the violet line is due to the transition from the sixth level (n=6) to the second level.

Key concepts

Hydrogen Line Spectrum

The hydrogen line spectrum is a fascinating phenomenon that arises from transitions of electrons within a hydrogen atom. When viewed through a prism, this spectrum appears as distinct colored lines against a dark background. It is a perfect example of how quantum mechanics works in atomic systems. These colors correspond to various wavelengths of light, each produced by electrons moving between different energy levels within the atom.
The spectrum is unique for hydrogen and serves as a fingerprint to identify its presence. This is why scientists can determine the composition of distant stars simply by studying their light. Each transition, from a higher to a lower energy level, generates a specific line in the spectrum, with distinct colors like red, turquoise, blue, and violet seen prominently in hydrogen's emission. These lines are crucial for understanding the structure of atoms and validating the Bohr model.

Energy Level Transitions

In the Bohr model, electrons occupy specific energy levels, or shells, around the nucleus. These levels are quantized, meaning electrons can only exist in these fixed states and nowhere in between. When an electron loses energy, it moves from a higher energy level to a lower one, a process known as an electron transition.
The energy lost by the electron gets released as a photon, and the amount of energy emitted corresponds precisely to the difference between the two energy levels. The energy difference is crucial as it determines the wavelength - and thus the color - of the emitted light. For hydrogen, these transitions from higher energy levels to the second level explain the visible lines in its spectrum. This concept is key to all spectroscopic studies and helps illuminate the quantum nature of light and matter.

Electron Orbits

Electron orbits in the Bohr model are reminiscent of planets orbiting the sun, though they are governed by the principles of quantum mechanics rather than classical physics. Each orbit corresponds to a specific energy level, and an electron in orbit surrounds the nucleus at a particular distance determined by that energy level.
This model introduces the idea that electrons can jump between orbits by absorbing or emitting energy. In their normal state, electrons occupy the lowest energy orbit possible, known as the ground state. By gaining energy, they can move to higher energy orbits, leading to what is called an excited state. Upon returning to a lower orbit, the electron releases energy as a photon, producing spectral lines that represent the distinct energy transitions.

Photon Emission

Photon emission is at the heart of understanding how atoms interact with light. In the Bohr model, when an electron transitions from a higher to a lower energy level, it emits a photon - a particle of light - with energy that matches the difference between the two levels.
These emitted photons are responsible for the atomic spectra, which appear as discrete lines of specific colors for hydrogen. The energy of each photon can be calculated using the formula: \[ E = hf \] where \( E \) is the energy of the photon, \( h \) is Planck's constant, and \( f \) is the frequency of the emitted light.
Understanding photon emission is fundamental to many technologies and scientific techniques such as lasers, LEDs, and spectroscopy, and it provides insight into the quantized nature of atomic energy levels.