Practice portal › Atoms › Bohr Model of the Hydrogen Atom
Asked in GSEB Board July 2016 · Energy levels and ionisation
Given: two hydrogen-like ions with V_B>V_A. Ionisation is from the ground state, so r means the ground-state orbit radius.
Idea: for a one-electron ion of atomic number Z, Bohr's model gives V=13.6 Z² V and r=(a₀)/Z in the ground state.
A larger ionisation potential means a larger Z: V_B>V_A gives Z_B>Z_A.
A larger Z means a smaller orbit, so r_B<r_A.
Put together, V∝1/(r²): the ion with the higher ionisation potential has the smaller radius.
Therefore r_A>r_B.
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