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Structure of Atom question

2024 · 6 Apr · Shift 2 · Q24
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Structure of Atom question

2024 · 6 Apr · Shift 2 · Q24

JEE MainChemistryStructure of AtomNumerical+4 / −1
For hydrogen atom, energy of an electron in first excited state is −3.4 eV,K.E-3.4 \mathrm{~eV}, \mathrm{K} . \mathrm{E}−3.4 eV,K.E. of the same electron of hydrogen atom is x eVx \mathrm{~eV}x eV. Value of xxx is ‾\underline{\hspace{2cm}}​×10−1 eV\times 10^{-1} \mathrm{~eV}×10−1 eV. (Nearest integer)
Numerical answer
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Correct answer: 34

  1. For a hydrogen atom, the total energy of an electron is E=K.E.+P.E.E = K.E. + P.E.E=K.E.+P.E. Using Bohr model results, P.E.=−2(K.E.)P.E. = -2(K.E.)P.E.=−2(K.E.) So, E=K.E.−2(K.E.)=−K.E.E = K.E. - 2(K.E.) = -K.E.E=K.E.−2(K.E.)=−K.E. Hence, K.E.=−EK.E. = -EK.E.=−E

  2. The electron is in the first excited state, so its energy is given as E=−3.4 eVE = -3.4\,\text{eV}E=−3.4eV Therefore, K.E.=−(−3.4)=3.4 eVK.E. = -(-3.4) = 3.4\,\text{eV}K.E.=−(−3.4)=3.4eV

  3. The question says x×10−1 eV=3.4 eVx\times 10^{-1}\,\text{eV} = 3.4\,\text{eV}x×10−1eV=3.4eV So, x=3.410−1=34x = \frac{3.4}{10^{-1}} = 34x=10−13.4​=34

  4. Nearest integer: x=34x = 34x=34

Therefore, the required value is 34\boxed{34}34​

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