Question

a hydrogen - like ion is an ion containing only one electron. the energies of the electron in a hydrogen - like ion are given by
e_{n}=-left(2.180 \times 10^{-18} mathrm{~j}
ight) z^{2}left(\frac{1}{n^{2}}
ight)
where ( n ) is the principal quantum number, and ( z ) is the atomic number of the element. calculate the ionization energy, in ( \frac{mathrm{kj}}{mathrm{mol}} ), of the ( mathrm{he}^{+} )ion. be sure your
answer has the correct number of significant digits.
note: reference the fundamental constants table for additional information.

Explanation:

Step1: Determine the values of \(n\) and \(Z\)

For ionization energy, the electron is removed from the ground - state (\(n = 1\)). For \(He^{+}\), the atomic number \(Z=2\).

Step2: Calculate the energy of the electron in the ground - state

Substitute \(n = 1\) and \(Z = 2\) into the formula \(E_{n}=-(2.180\times 10^{-18}\ J)Z^{2}(\frac{1}{n^{2}})\)

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Step3: Calculate the ionization energy per atom

The ionization energy per atom \(IE\) is the energy required to remove the electron, so \(IE=\vert E_{1}\vert=8.72\times 10^{-18}\ J\)

Step4: Convert the ionization energy per atom to ionization energy per mole

Use Avogadro's number \(N_{A}=6.022\times 10^{23}\ mol^{-1}\)

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Answer:

\(5250\ kJ/mol\) (rounded to three significant digits)