Question

According to Bohr, what happens to the electron when a hydrogen atom absorbs a photon of light of sufficient energy?

Short answer

When a hydrogen atom absorbs a photon of light with sufficient energy according to Bohr's model, the electron in the atom gets excited and moves from a lower energy orbit to a higher energy orbit. This process is called excitation. Eventually, the electron loses the excess energy, returning to a lower energy orbit and emitting a photon with a frequency corresponding to the energy difference between the orbits.

Step-by-step solution

Understand Bohr's model of a hydrogen atom

Bohr's model of a hydrogen atom consists of a nucleus containing a single proton, with a single electron orbiting around it in quantized energy levels called orbits. These orbits are at fixed distances from the nucleus and have specific energy levels associated with them. The electron can only be in one of these orbits and cannot exist between them. When a photon of light interacts with the hydrogen atom, it can cause the electron to change its orbit if the photon has enough energy.

Determine the energy required for an electron to move between orbits

When an electron absorbs a photon of light, the energy of the photon is transferred to the electron. The energy (E) of the photon can be calculated using Planck's equation \(E = h \times \nu\), where 'h' is Planck's constant and '\(\nu\)' is the frequency of the light. The energy required for an electron to move between orbits can be calculated using the following equation: \[\Delta E = E_{n2} - E_{n1} = -13.6 \times \frac{1}{n2^2} - \left( -13.6 \times \frac{1}{n1^2} \right)\] Here, \(\Delta E\) is the energy difference between the two orbits (orbit \(n1\) and orbit \(n2\)), and the energy levels \(E_{n1}\) and \(E_{n2}\) are expressed in electron volts (eV). The electron can only move between orbits if the energy of the incoming photon equals the energy difference between the orbits.

Describe the process when the electron absorbs the photon

When a hydrogen atom absorbs a photon of light with sufficient energy, the electron in the hydrogen atom moves from a lower energy orbit (initial orbit) to a higher energy orbit (final orbit). This process is called excitation, and the energy of the photon must be equal to the energy difference between the initial and final orbits for the electron to be excited.

Explain what happens after the electron has been excited

After the electron has absorbed the photon and moved to a higher energy orbit, it is in an unstable and excited state. Eventually, the electron will lose the excess energy and return to a lower energy orbit (the ground state or another lower energy orbit), releasing a photon of light in the process. This emitted photon's energy will be equal to the energy difference between the orbits, and its frequency will be determined by the energy difference, as described by Planck's equation. This process is called de-excitation. In conclusion, according to Bohr's model, when a hydrogen atom absorbs a photon of light of sufficient energy, the electron in the atom gets excited and moves from a lower energy orbit to a higher energy orbit. Then, it eventually loses the excess energy, returning to a lower energy orbit as it emits a photon with a frequency corresponding to the energy difference between the orbits.

Key concepts

Energy Levels in Atoms

Picture an atom as a tiny but bustling city, with roads that the electrons can travel on. However, these roads are not continuous but are rather like distinct circular tracks, each positioned at a specific distance from the atomic nucleus, which is at the very heart of the atom's city. These tracks are known as energy levels, and they're crucial because they dictate how the atom behaves and reacts with others.

Each track has its own energy, and an electron can only 'run' on these specific tracks — or energy levels. But here's the trick: unlike a car, the electron can't just move from one track to another smoothly; it needs a sort of 'energy ticket' to jump between them. This 'ticket' comes in the form of photons, or light particles. The amount of energy in the 'ticket' must exactly match the difference between the energy levels for the electron to make the move. If it doesn't, the electron remains in its lane, unchanged.

Photon Absorption and Emission

Let's turn our attention to how atoms interact with light. Light consists of particles called photons, and when an atom encounters a photon, it's a bit like when you get a surprise package. If the 'package'— or in this case, the photon — is exactly what the atom's electron needs (in terms of energy), the electron accepts it. This is photon absorption. But, electrons can't hold on to this energy forever. Like a hot potato, the electron eventually wants to drop this extra energy and return to a more comfortable, lower energy level. When it does so, it sends out a new photon into the space — this is photon emission.

The colors of light we see are actually photons being emitted at different energies (which we perceive as different colors). So when you see the brilliant red of a laser or the deep blue of a flame, you're witnessing atoms emitting photons as their electrons drop down from high-energy highways to more relaxed lanes.

Quantum Excitation and De-excitation

Now imagine electrons within an atom as being a bit like people on a ladder; to get to a higher rung, you need to put in the effort to climb up. In a similar sense, when an electron gains the right amount of energy (through that precise 'energy ticket' from a photon), it climbs up to a higher-energy level — this is known as quantum excitation.

However, being on a higher rung can be tiring for an electron, just as it would be for a person, and they don't stay there indefinitely. When they 'climb' back down, they release the extra energy that they absorbed earlier. This 'climb' back down to a more stable, lower energy level is the de-excitation process. The electron doesn’t just shed any arbitrary amount of energy when it does this; it lets go of precisely the amount that equates to the distance it dropped on the 'energy ladder.' This released energy is observed as a photon — a fundamental process behind fascinating things like neon signs and stars shining in the night sky.