HardChemistryHigh School (11–12)Structure of the Atom › Light, Atomic Spectra and the Bohr ModelNumerical

The ion He⁺ has one electron. Find the wavelength of the photon given out when its electron falls…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The ion $\text{He}^+$ has one electron. Find the wavelength of the photon given out when its electron falls from $n = 4$ to $n = 3$ . How does it compare with the same jump in hydrogen, and in which part of the spectrum does each lie?

Need a reminder? The key ideaShow

For a one-electron atom: $r_n = 52.9\ \text{pm} \times \dfrac{n^2}{Z}$ , $E_n = -13.6\ \text{eV} \times \dfrac{Z^2}{n^2}$ , $v_n = 2.19 \times 10^{6}\ \text{m s}^{-1} \times \dfrac{Z}{n}$ . A jump gives a photon of energy $E_{\text{high}} - E_{\text{low}}$ . $1\ \text{eV per atom} = 96.485\ \text{kJ mol}^{-1}$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← For the electron in the n = 4 orbit of a hydrogen atom, find these.Find the energy needed to remove the electron from B⁴⁺, with Z = 5, in its ground state. →

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