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Atoms — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAtoms3 Marks
Question
Define ionisation energy.
When in a hydrogen atom an electron is replaced by such a particle whose mass is 200 times the mass of the electron and its charge is the same as that of electron, then how will its ionisation energy be changed ?
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Answer

Ionisation Energy : The process of knocking an electron out of the atom is called ionisation. After ionisation the residual hydrogen atom becomes positively charged with positive charge equal to charge of one electron i.e. $1.6\times10^{-19}$ coulomb i.e. it becomes positive ion. Hence the process is given the name as ionisation.
Ionisation energy is defined as the energy required to knock an electron completely out of the atom.
When an electron is raised from $n=1$ to $n=\infty$, then it will be completely out of the atom i.e. the atom will be ionised. Therefore ionisation energy of hydrogen atom is equal to the energy required to raise it from orbit $n=1$ to $n=\infty$, i.e.
Ionisation energy $= E_{\infty}-E_{1}=0-(-13.6)=13.6$ eV
Ionisation energy in a hydrogen atom is expressed as:
$\frac{me^{4}}{8\in_{0}^{2}h^{2}}$
⇒ Ionisation Energy $\propto m$ (while charge 'e' is same for particle as for electron i.e. e)
Hence when the electron in hydrogen atom is replaced by a particle of mass 200 times the mass of the electron then its ionisation energy will become 200 times that for hydrogen atom.

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