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**Advanced Higher Chemistry**

Unit 1 The Hydrogen Spectrum

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**Emission Spectrum of hydrogen**

When a high voltage is passed through a sample of hydrogen gas at low pressure, a coloured light is produced. When this coloured light is passed through a diffraction grating, coloured lines corresponding to certain frequencies of wavelengths are seen.

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**Absorption spectra of hydrogen in the visible region**

Emission spectra of hydrogen in the visible region

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Hydrogen has only one electron suggesting that its emission spectrum should be easiest to interpret. However, its spectrum is still very complicated. Each line in the hydrogen emission spectrum corresponds to the energy given out when an excited electron falls back to the lowest energy level known as ground state (n=1).

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There are other series of lines corresponding to excited electrons falling back to the n=5, n=4, n=3 (lines are produced in the IR region) and n=1 energy levels (lines are produced in the UV region).

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Hydrogen

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**Electrons falling to n = 1 Lyman UV**

Electrons falling to n = 2 Balmer Visible Electrons falling to n = 3 Paschen IR Electrons falling to n = 4 Brackett IR Electrons falling to n = 5 Pfund IR Lowest energy level (n = 1) - ground state Higher energy levels (n >1) - excited state

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The Convergence Limit At higher energies the energy levels further from the nucleus become closer and closer together so the lines for a particular series also become closer and closer together until they merge into a continuum. This continuum is known as the convergence limit. The electron has escaped from the atom (i.e. has undergone ionisation) at the convergence limit and hence the convergence frequency can be used to find the ionisation energy of the atom.

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Bohr Theory The electron in a hydrogen atom exists only in certain definite energy levels. A photon of light is emitted or absorbed when the electron changes from one energy level to another. Energy of one photon is equal to the difference between the two energy levels (this can be related to frequency).

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The relationship between the energy change in the particle and the frequency of radiation emitted or absorbed is given by: ΔE = hf or ΔE = hc λ

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**For one mole of particles**

ΔE = Lhf or ΔE = Lhc λ

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**Exercise The convergence limit in the Lyman series is 91.2nm.**

Calculate the energy, in kJmol-1, corresponding to the wavelength of this convergence limit. HINT If you have the correct answer it should be the same value as the ionisation energy for hydrogen

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