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Structure of Atom — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistryStructure of Atom3 Marks
Question
Calculate the energy required for the process,
$\text{He}^+(\text{g})\rightarrow\text{He}^{2+}\text{(g)}+\text{e}^-$
The ionization energy for the H atom in the ground state is $2.18 \times 10^{-18} \mathrm{~J}\mathrm{~atom}^{-1}$
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Answer

Energy associated with hydrogen-like species is given by,
$\text{E}_{\text{n}}=-2.18\times10^{-18}\Big(\frac{\text{Z}^2}{\text{n}^2}\Big)\text{J}$
For ground state of hydrogen atom,
$\triangle\text{E = E}_{\infty}-\text{E}_1$
$=0-\bigg[-2.18\times10^{-18}\bigg\{\frac{(1)^2}{(1)^2}\bigg\}\bigg]\text{J}$
$\triangle\text{E}=2.18\times10^{-18}\text{J}$
For the given process,
$\text{He}^+(\text{g})\rightarrow\text{He}^{2+}\text{(g)}+\text{e}^-$
An electron is removed from $\text{n}=1\text{ to}\text{ n}=\infty.$
$\triangle\text{E = E}_{\infty}-\text{E}_1$
$=0-\bigg[-2.18\times10^{-18}\bigg\{\frac{(2)^2}{(1)^2}\bigg\}\bigg]$
$\triangle\text{E}=8.27\times10^{-18}\text{J}$
$\therefore$ The energy required for the process $8.27\times10^{-18}\text{J}.$

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