A ground state hydrogen atom absorbs a photon of light having a wavelength of 97.2 nm. It then

A ground state hydrogen atom absorbs a photon of light...

Key Concepts

Quantum Energy Levels

In the hydrogen atom, electrons exist in discrete energy levels, each defined by a principal quantum number (n). These quantized energy states mean that an electron can only possess certain specified energies, and transitions between these levels result in the absorption or emission of photons whose energies match the difference between the levels.

Photon Absorption and Emission

When a photon is absorbed by a hydrogen atom, its electron is excited from a lower energy level to a higher one. Conversely, when the electron drops from a higher level to a lower level, a photon is emitted. The energies of these photons are directly proportional to the difference in energy between the two involved states, illustrating the conservation of energy in the process.

Rydberg Formula

The Rydberg formula relates the wavelength of light absorbed or emitted by hydrogen to the electron transitions between energy levels. This formula provides a way to calculate the wavelengths based on the starting and ending quantum numbers, and is fundamental in analyzing the spectral lines of hydrogen.

Electron Transitions (Spectral Series)

Electron transitions in hydrogen result in characteristic spectral lines, as observed in series such as the Lyman and Balmer series. For example, a transition from a higher level down to n=2 is part of the Balmer series, which produces visible light. Recognizing which transitions correspond to specific wavelengths allows determination of the initial and final states of the electron.

Transcript

00:01 In this question we've been given a hydrogen atom that was initially at ground state and it absorbed a photon of a certain wavelength and that wavelength is 97 .2.

00:13 Up to a certain level, let's just call this nx and then it released a photon of a wavelength of 7 or rather 486 up to a certain level.

00:29 So we want to determine the value of n at this level.

00:33 So what we can do is to first of all look at, look for this value, nx, and then look at the final value.

00:40 Let's just call this ny.

00:42 And the information that we've been given, we've been given wavelengths and we want to determine the n final.

00:48 And the one parameter that we know that links all of these, these two variables is the energy.

00:54 So we first of all calculate the energy associated with this absorption of the first of all, photon and the release of a photon at 486 for us then determine our nf.

01:06 Now looking at this, let's just make half our formulas, the energy.

01:13 This is equal to hc divided by the wavelength.

01:18 But we also know that the energy when we are looking at a hydrogen atom, this is 2 .1799 a j multiplied by 1 divided by n squared initial minus 1.

01:30 1 divided by n squared final.

01:34 So what we are interested in in both cases is this end.

01:38 We are going to split this calculation into two phases.

01:42 That is we look at the first absorption of the photon and the second phase of the release of another photon...

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