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The ion Li²⁺ has one electron and a nucleus with Z = 3…

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The ion $\text{Li}^{2+}$ has one electron and a nucleus with $Z = 3$ . For the level $n = 5$ find (a) the radius of the orbit, in nm, (b) the speed of the electron, in units of $10^6\ \text{m/s}$ , and (c) the total energy, in eV.

Need a reminder? The key ideaShow

For one electron and a nucleus of charge $Ze$ : $r_n = \dfrac{0.0529\ \text{nm}\,n^2}{Z}$ , $v_n = \dfrac{2.19 \times 10^6\ \text{m/s}\,Z}{n}$ and $E_n = -\dfrac{13.6\ \text{eV}\,Z^2}{n^2}$ .

\displaystyle h\nu = E_i - E_f

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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