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Basic Ideas About Atoms

The hydrogen spectrum, E = hf and the convergence limit

  • 3 things to know
  • Components 1 and 2

Overview

Convergence limit of a spectral series, relationship between the frequency and the wavelength of electromagnetic radiation and seen beyond the convergence limit of a series.

What you need to know

Answer each one before you reveal it.

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Key term

State the relationship between the energy of a photon and its frequency, naming the constant.

Numbers

Calculate the energy of a single photon of frequency 3.00 × 10¹⁵ Hz.

Numbers

Calculate the frequency of light of wavelength 4.50 × 10⁻⁷ m.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    At which energy level do the transitions of the Lyman series end, and in which region of the spectrum do they lie?

    Model answer

    They end at n = 1 and lie in the ultraviolet region.

  2. 2

    At which level do the transitions of the Balmer series end, and where do they appear?

    Model answer

    They end at n = 2 and appear in the visible region.

  3. 3

    At which level do the transitions of the Paschen series end, and where do they appear?

    Model answer

    They end at n = 3 and appear in the infrared region.

  4. 4

    Why is the Lyman series the highest in energy of the hydrogen series?

    Model answer

    Its transitions end at the lowest energy level of all, so they involve the largest drops in energy and therefore the highest frequencies.

  5. 5

    What is meant by the convergence limit of a spectral series?

    Model answer

    It is the frequency at which the lines become so closely spaced that they merge, corresponding to a transition involving the level n = ∞.

  6. 6

    What physical event does the convergence limit of the Lyman series correspond to?

    Model answer

    It corresponds to the electron being removed altogether from the n = 1 level, which is the ionisation of a hydrogen atom in its ground state.

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