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Structure of Atom question

2023 · 13 Apr · Shift 1 · Q13
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Structure of Atom question

2023 · 13 Apr · Shift 1 · Q13

JEE MainChemistryStructure of AtomMCQ+4 / −1
The energy of an electron in the first Bohr orbit of hydrogen atom is −2.18×10−18 J-2.18 \times 10^{-18} \mathrm{~J}−2.18×10−18 J. Its energy in the third Bohr orbit is ‾\underline{\hspace{2cm}}​.
  1. A
    One third of this value
  2. B
    Three times of this value
  3. C
    19\frac{1}{9}91​ th of this value
  4. D
    127\frac{1}{27}271​ of this value
View written solutionFree

Correct answer: C

  1. Bohr energy formula

    For hydrogen atom, the ऊर्जा of the electron in the nnnth Bohr orbit is En=−2.18×10−18n2 JE_n = \frac{-2.18 \times 10^{-18}}{n^2}\ \text{J}En​=n2−2.18×10−18​ J

  2. Given energy in first orbit

    For n=1n=1n=1, E1=−2.18×10−18 JE_1 = -2.18 \times 10^{-18}\ \text{J}E1​=−2.18×10−18 J

  3. Energy in third orbit

    For n=3n=3n=3, E3=E132=E19E_3 = \frac{E_1}{3^2} = \frac{E_1}{9}E3​=32E1​​=9E1​​

    Therefore, E3=−2.18×10−189 JE_3 = \frac{-2.18 \times 10^{-18}}{9}\ \text{J}E3​=9−2.18×10−18​ J

  4. Compare with options

    • A: One third of this value →\rightarrow→ incorrect
    • B: Three times of this value →\rightarrow→ incorrect
    • C: 19\frac{1}{9}91​th of this value →\rightarrow→ correct
    • D: 127\frac{1}{27}271​ of this value →\rightarrow→ incorrect

  5. Final answer

    The energy in the third Bohr orbit is 19\frac{1}{9}91​th of the energy in the first orbit (same negative sign retained), i.e. E3=−2.42×10−19 JE_3 = -2.42 \times 10^{-19}\ \text{J}E3​=−2.42×10−19 J

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