An electron accelerates through a 12.5 V potential difference, starting from rest, and then col

step 1 This is the energy level diagram for hydrogen atom. Here the energy difference between n -equal

An electron accelerates through a 12.5 V potential...

An electron accelerates through a $12.5 \mathrm{~V}$ potential difference, starting from rest, and then collides with a hydrogen atom, exciting the atom to the highest energy level allowed. List all the possible quantum-jump transitions by which the excited atom could emit a photon and the wavelength (in nm) of each.

Key Concepts

Photon Emission and Wavelength Determination

The energy difference between the two energy levels during a transition is released as a photon. The wavelength of the emitted photon is calculated using the relationship between energy and wavelength, generally determined by converting energy differences into photon wavelengths via the equation ? = hc/?E.

Rydberg Formula

The Rydberg formula provides a way to calculate the wavelengths of photons emitted or absorbed during transitions between energy levels in hydrogen-like atoms. By specifying the initial and final quantum numbers, the formula directly relates these numbers to the resulting spectral lines, which helps in predicting the possible photon wavelengths emitted during quantum transitions.

Quantum Transitions

Once an atom is excited, electrons will eventually transition back to lower energy states. These quantum jumps occur in multiple possible pathways, each corresponding to a specific energy difference. The energy lost in these transitions is emitted as a photon, and different transitions produce photons of different energies.

Collision?Induced Excitation

During collisions, a fast-moving electron can transfer part or all of its kinetic energy to an atom, causing its electrons to move to higher energy levels. The amount of energy transferred determines which excited states are reached, affecting the subsequent photon emission when the electron relaxes.

Electron Acceleration and Potential Difference

When electrons are accelerated through a potential difference, they gain kinetic energy equal to the product of the electron charge and the voltage. This energy, measured in electron volts (eV), is crucial in processes such as excitation of atomic electrons during collisions.

Quantized Energy Levels

In atomic physics, atoms such as hydrogen have discrete energy states determined by quantum numbers. Electrons in an atom can only reside in these fixed energy levels, and any transition between them involves the absorption or emission of energy corresponding to the difference between these levels.

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