Question 19N.2.HL.TZ0.8

equating centripetal to electrical force $\frac{2k{e}^2}{r^2}=\frac{m{v}^2}{r}$ to get result ✔

uses (a)(i) to state $E_{\mathrm{k}}=\frac{k{e}^2}{r}$ OR states $E_{\mathrm{p}}=-\frac{2k{e}^2}{r}$ ✔

adds « $E_{\mathrm{TOT}}=E_{\mathrm{k}}+E_{\mathrm{p}}=\frac{k{e}^2}{r}-\frac{2k{e}^2}{r}$» to get the result ✔

the total energy decreases
OR
by reference to $E_{\mathrm{TOT}}=-\frac{k{e}^2}{r}$ ✔

the radius must also decrease ✔

NOTE: Award [0] for an answer concluding that radius increases

with $n=3, v=«\sqrt{\frac{2\times 8.99\times {10}^9\times {\left(1.6\times {10}^{-19}\right)}^2}{9.11\times {10}^{-31}\times 9\times 2.7\times {10}^{-11}}}=» 1.44\times {10}^6 «\mathrm{m} {\mathrm{s}}^{-1}»$✔

$\lambda =\frac{6.63\times {10}^{-34}}{9.11\times {10}^{-31}\times 1.44\times {10}^6}$  OR  $\lambda =5.05\times {10}^{-10} «\mathrm{m}»$✔

$\frac{{\displaystyle 2\pi r}}{{\displaystyle \lambda }}=«\frac{{\displaystyle 2\pi \times 9\times 2.7\times {10}^{-11}}}{{\displaystyle 5.1\times {10}^{-10}}}=2.99»\cong 3$ ✔

NOTE: Allow ECF from (b)(i)

reference to fixed orbits/specific radii OR quantized angular momentum in Bohr model ✔

electron described by a wavefunction/as a wave in Schrödinger model OR as particle in Bohr model ✔

reference to «same» energy levels in both models ✔

reference to «relationship between wavefunction and» probability «of finding an electron in a point» in Schrödinger model ✔