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JEE Main 2023 · Physics · Atoms, Nuclei and Dual Nature of Radiation · easy

The electron in a doubly ionised lithium ion (Li^2+) drops from the n=3 level to n=2. The emitted photon falls on a stationary hydrogen atom in its…

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The electron in a doubly ionised lithium ion (Li2+\mathrm{Li^{2+}}) drops from the n=3n=3 level to n=2n=2. The emitted photon falls on a stationary hydrogen atom in its ground state and ionises it. The kinetic energy of the ejected electron is (ground-state energy of hydrogen =−13.6 eV=-13.6\ \mathrm{eV})
  1. A. 3.4 eV3.4\ \mathrm{eV}
  2. B. 1.9 eV1.9\ \mathrm{eV}
  3. C. 17.0 eV17.0\ \mathrm{eV}
  4. D. 30.6 eV30.6\ \mathrm{eV}
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Answer: (A) 3.4 eV3.4\ \mathrm{eV}

For a hydrogen-like ion En=−13.6 Z2/n2E_n=-13.6\,Z^2/n^2 eV. For Li2+\mathrm{Li^{2+}} (Z=3Z=3): Ephoton=13.6×9(14−19)=13.6×9×536=17.0 eVE_{photon}=13.6\times9\left(\dfrac14-\dfrac19\right)=13.6\times9\times\dfrac5{36}=17.0\ \mathrm{eV}. Ionising hydrogen from the ground state needs 13.6 eV13.6\ \mathrm{eV}, so the photoelectron has K=17.0−13.6=3.4 eVK=17.0-13.6=3.4\ \mathrm{eV}.
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