Consider the Bohr energy expression (Equation 30.13) as it applies to singly ion

Question

Consider the Bohr energy expression (Equation 30.13) as it applies to singly ionized helium He+ (Z = 2) and an ionized atom with Z=5 and only a single electron orbiting the nucleus. This expression predicts equal electron energies for these two species for certain values of the quantum number n (the quantum number is different for each species). For quantum numbers less than or equal to 9, what is the highest energy (in electron volts) for which the heluim energy level is equal to the ionized atom energy level?

Explanation / Answer

En = (-13.6eV)(Z2/n2)

25/(nx)2 = (4/nHe)2

5/nx = 2/nHe

5nHe = 2nx thus the lowest valuewhich satisfy is only nHe = 2

En = (-13.6eV)(Z2/n2)

En = (-13.6eV)(22/22)

En = -13.6eV

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