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The electron in a hydrogen atom makes a transition n1 ¾→ n2, where n1 & n2 are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n1 & n2 are :
  • a)
     n1 = 4, n2 = 2
  • b)
    n1 = 8, n2 = 2 
  • c)
    n1 = 8, n2 = 1
  • d)
    n1 = 6, n2 = 3
Correct answer is option 'A,D'. Can you explain this answer?
Verified Answer
The electron in a hydrogen atom makes a transition n1¾→n2,...
For an electron revolving in nth orbit around the nucleus of hydrogen atom, Fcentrifugal​=Fcoulomb​
Thus,  mvn2/ rn​​​=​e2​/4πϵo​rn2
Also, mvn​rn​=nh/2π​
On solving these two we get: vn​= e21/2ϵo​hn ​and rn​=( ϵo​h2/πme2 ​) n2 
Time period, T=2πrn/vn​​​⟹T∝n3
Thus, 8T/T​=(​n1/n2)3⟹n1​=2n2
Thus, n1​=4,n2​=2  and   n1​=6,n2​=3 
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The electron in a hydrogen atom makes a transition n1¾→n2,...
It seems like there is a typo or incomplete information in the question. The sentence ends with "n1" and doesn't specify what happens with the transition. Please provide additional information so I can properly answer the question.
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The electron in a hydrogen atom makes a transition n1¾→n2,...
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The electron in a hydrogen atom makes a transition n1¾→n2, where n1& n2are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n1& n2are :a)n1= 4, n2= 2b)n1= 8, n2= 2c)n1= 8, n2= 1d)n1= 6, n2= 3Correct answer is option 'A,D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The electron in a hydrogen atom makes a transition n1¾→n2, where n1& n2are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n1& n2are :a)n1= 4, n2= 2b)n1= 8, n2= 2c)n1= 8, n2= 1d)n1= 6, n2= 3Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The electron in a hydrogen atom makes a transition n1¾→n2, where n1& n2are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n1& n2are :a)n1= 4, n2= 2b)n1= 8, n2= 2c)n1= 8, n2= 1d)n1= 6, n2= 3Correct answer is option 'A,D'. Can you explain this answer?.
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