Q47 / 54 · JEE Advanced 2016 (Paper 1) · Physics

Highly excited states for hydrogen like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >> 1. Which of the following statement(s) is (are) true?

  • Correct answer
    A
    Relative change in the radii of two consecutive orbitals does not depend on Z
  • Correct answer
    B
    Relative change in the radii of two consecutive oribitals varies as 1/n
  • C
    Relative change in the energy of two consecutive orbitals varies as 1/ n3
  • Correct answer
    D
    Relative change in the angular momenta of two consecutive orbitals varies as 1/n

Solution

As radius r ∝n2z0
⇒  ∆rr=n+1z2-nz2nz2=2n+1n2≈2n∝1n
As energy E ∝z2n2
⇒  ∆EE=z2n2-z2n+12z2n+12=n+12-n2n2.n+12. n+12
⇒  ∆EE=2n+1n2≃2nn2∝1n
As angular momentum L=nh2π
⇒  ∆LL=n+1h2π-nh2πnh2π=1n ∝1n

Hence, the correct answer is options: 'A', 'B', 'D'.

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