How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom (energy required to remove the electron from n = 1 orbit).

Solution

straight E subscript 1 space equals space minus 2.18 space cross times space 10 to the power of negative 18 end exponent straight J space atm to the power of negative 1 end exponent straight E subscript 5 space equals space minus fraction numerator 2.18 space cross times space 10 to the power of negative 18 end exponent over denominator left parenthesis 5 right parenthesis squared end fraction straight J space atm to the power of negative 1 end exponent space space space space space equals negative 8.72 space cross times space 10 to the power of negative 20 end exponent straight J space space atm to the power of negative 1 end exponent

Energy required to remove the electron from 5th orbit

equals space straight E subscript infinity space minus space straight E subscript 5 space equals space 0 minus left parenthesis negative 8.72 space cross times space 10 to the power of negative 20 end exponent straight J right parenthesis equals 8.72 space cross times 10 to the power of negative 20 end exponent

Energy required to remove the electron from n = 1 orbit

equals space straight E subscript infinity space minus space straight E subscript 1 space equals 0 minus left parenthesis negative 2.18 space cross times space 10 to the power of negative 18 end exponent straight J right parenthesis equals plus 2.18 space cross times space 10 to the power of negative 18 end exponent straight J

therefore space space IE subscript 5 over IE subscript 1 space equals space fraction numerator 8.72 space cross times space 10 to the power of negative 20 end exponent straight J over denominator 2.18 cross times 10 to the power of negative 18 end exponent straight J end fraction space equals space 4 space cross times space 10 to the power of negative 2 end exponent

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