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BITSAT 2024
Exam
BITSAT
Year
2024
Subject
Chemistry
Chapter
Structure of Atom

BITSAT 2024 · Chemistry · Structure of Atom

The degeneracy of hydrogen atom that has energy equal to -R_ H 9 is...

The degeneracy of hydrogen atom that has energy equal to −RH9\frac{-R_{\mathrm{H}}}{9} is (where, RH=R_{\mathrm{H}}= Rydberg constant)

Options

  1. A6
  2. B8
  3. C5
  4. D9

Correct answer

D. 9

Step-by-step solution

The energy is given as, E=−RH9...(i)E=-\frac{R_{\mathrm{H}}}{9}...(i) We know that, En=−RHn2...(ii)n2=9n=3\begin{aligned} E_n & =-\frac{R_{\mathrm{H}}}{n^2}...(ii)\\ n^2 & =9 \\ n & =3 \end{aligned} When n=3,l=0,1,2(3s,3p,3d sub-shells) Orbitalspresent(i.e.,degeneracy),n=3, l=0,1,2(3 s, 3 p, 3 d \text{ sub-shells) } Orbitals present (i.e., degeneracy),3 s=1,3 p=3,3 d=5TotalnumberoforbitalpresentTotal number of orbital present=3+1+5=9
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