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Q.

An electron is in an excited state in a hydrogen like atom. It has a total energy of -3.4 eV. The kinetic energy of electron is E and its de Broglie wavelength is λ

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a

E=6.8eV; λ=6.6×10−10m

b

E=3.4eV; λ=6.6×10−10m

c

E=3.4eV; λ=6.6×10−11m

d

E=6.8eV; λ=6.6×10−11m

answer is B.

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Detailed Solution

Potential energy =−2× Kinetic energy =−2E Total energy =−2E+E=−3.4eV=−E or  E=3.4eVp= momentum, m= mass of electron E=p22m or  p=2mE =2×9.1×10−31×3.4×1.6×10−19≈10−24 de Brogile wavelength λ=hp=h2mE=6.6×10−10
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