A photon of wavelength 320 nm is absorbed by a hydrogen atom when the electron is in the second

step 1 In this question, we have a hydrogen atom where the electrons in the second excited state, and i

A photon of wavelength 320 nm is absorbed by a hydrogen atom...

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Key Concepts

Kinetic Energy and Electron Speed

The relationship between kinetic energy and speed is given by the classical formula KE = ½ mv², where m is the mass of the electron. This equation is used to calculate the speed of the electron once its kinetic energy is determined from the energy surplus after ionization.

Ionization and Conservation of Energy

Ionization occurs when a photon provides enough energy to free an electron from its bound state in an atom. The excess energy (the difference between the photon energy and the binding energy of the electron) is converted into kinetic energy of the ejected electron, in accordance with the law of conservation of energy.

Hydrogen Atom Energy Levels

In quantum mechanics, electrons in a hydrogen atom occupy discrete energy levels characterized by the principal quantum number (n), with energy given by E = -13.6 eV/n². This quantization is fundamental in determining the energy difference required to excite or ionize an electron from a specific level.

Photon Energy Calculation

A photon’s energy is inversely proportional to its wavelength, as described by the equation E = hc/?, where h is Planck's constant and c is the speed of light. This concept allows us to calculate the amount of energy transferred to an electron when the photon is absorbed.

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