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Question

If the energy of H - atom in the ground state is −E, the velocity of photo electron emitted when a photon having energy Ep striked a stationary Li2+ ion in ground state, is given by:

A
v=2(EpE)m
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B
v=2(Ep+9E)m
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C
v=2(Ep9E)m
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D
v=2(Ep3E)m
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Solution

The correct option is C v=√2(Ep−9E)mEnergy of electron in the ground state of H− atom =−E=−13.6×Z2n2=−13.6×1212=−13.6 eV Energy of electron in the ground state of Li2+ =−13.6×Z2n2=−13.6×3212=−9E (∵−13.6eV=−E) Energy supplied by photon =IE+12mv2 IE=−(−9E)=9E ∴Ep=9E+12mv2 ⇒v=√2(Ep−9E)m

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