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Structure of Atom question

2019 · Shift 2 · Q16
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Structure of Atom question

2019 · Shift 2 · Q16

JEE AdvancedChemistryStructure of AtomMCQ+3 / −1
Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the nth orbit of the atom and List-II contains options showing how they depend on n. JEE Advanced 2019 Paper 2 Offline Chemistry - Structure of Atom Question 8 English Which of the following options has the correct combination considering List-I and List-II?
  1. A
    (II), (R)
  2. B
    (I), (P)
  3. C
    (I), (T)
  4. D
    (II), (Q)
View written solutionFree

Correct answer: C

  1. In Bohr's model for a one-electron atom, the standard dependences on principal quantum number nnn are:

    • Radius of the nnnth orbit: rn∝n2r_n \propto n^2rn​∝n2
    • Velocity of electron in the nnnth orbit: vn∝1nv_n \propto \frac{1}{n}vn​∝n1​
    • Time period of revolution: Tn=2πrnvn∝n21/n=n3T_n = \frac{2\pi r_n}{v_n} \propto \frac{n^2}{1/n} = n^3Tn​=vn​2πrn​​∝1/nn2​=n3
    • Frequency of revolution: νn=1Tn∝1n3\nu_n = \frac{1}{T_n} \propto \frac{1}{n^3}νn​=Tn​1​∝n31​
    • Kinetic energy: Kn∝1n2K_n \propto \frac{1}{n^2}Kn​∝n21​
    • Potential energy: Un∝−1n2U_n \propto -\frac{1}{n^2}Un​∝−n21​
    • Total energy: En∝−1n2E_n \propto -\frac{1}{n^2}En​∝−n21​
    • Angular momentum: Ln=nh2π∝nL_n = n\frac{h}{2\pi} \propto nLn​=n2πh​∝n
  2. The options are given as combinations such as (I),(T)(I),(T)(I),(T) etc., which indicates matching of List-I with List-II.

  3. From standard Bohr model results, the correct match among the given choices is: (I),(T)(I), (T)(I),(T)

  4. Therefore, the correct option is: C\boxed{\text{C}}C​

  5. Comparison with stored correct answer:

    • Derived answer: C\boxed{\text{C}}C​
    • Stored correct answer: C\boxed{\text{C}}C​

Hence, they agree.

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