Chemistry

Problem

A general study of Bohr atoms requires a relation between the principal quantum number and the energy needed to free an electron. a. (a) Starting from the Bohr expression for the permitted energies of a one-electron atom, derive a formula for the ionisation energy

E_{\text{ion}}(n, Z)

needed to remove an electron that is initially in the

n^{\text{th}}

orbit of a hydrogen-like ion of atomic number

Z

. b. (b) Using the expression obtained in part (a), compute the energy in electronvolt required to ionise an electron from the third orbit (

n = 3

) of a

B^{4+}

ion (

Z = 5

). c. (c) Convert the result of part (b) to joule per mole. (Take

N_{A} = 6.02 \times 10^{23}\,\text{mol}^{-1}

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

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