Following Bohr, we assume that a hydrogen-like atom may be modelled as a single electron (mass...

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Following Bohr, we assume that a hydrogen-like atom may be modelled as a single electron (mass m and charge -e) in a circular orbit around a much more massive nucleus (charge +Ze). (a) By balancing forces, find the speed v of the electron in terms of its orbital radius. (b) Show that the total energy of the electron is equal to the negative of its kinetic energy. You may assume that its potential energy U is given by (where r is the radius of the orbit) (d) If E(n (He+)? (c) Assuming that for the electron the product mur = nħ, where n is an integer and ħ (pronounced h-bar) is a constant, find an expression for the electron energy in terms of n (and which does not depend on either v or r). 13.6 eV for hydrogen, what is E(n = 3) for once-ionised helium = U= 1) Ze² 4π€or [3] [3] [2] [2] Following Bohr, we assume that a hydrogen-like atom may be modelled as a single electron (mass m and charge -e) in a circular orbit around a much more massive nucleus (charge +Ze). (a) By balancing forces, find the speed v of the electron in terms of its orbital radius. (b) Show that the total energy of the electron is equal to the negative of its kinetic energy. You may assume that its potential energy U is given by (where r is the radius of the orbit) (d) If E(n (He+)? (c) Assuming that for the electron the product mur = nħ, where n is an integer and ħ (pronounced h-bar) is a constant, find an expression for the electron energy in terms of n (and which does not depend on either v or r). 13.6 eV for hydrogen, what is E(n = 3) for once-ionised helium = U= 1) Ze² 4π€or [3] [3] [2] [2]

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