Single correct option
Consider the ion () in the Bohr model, with its single electron in the stated state. Here is the Bohr radius and the ground-state energy of hydrogen is . Match List-I with List-II.
List-I
(P) Radius of the orbit with
(Q) Total energy of the electron for
(R) de Broglie wavelength of the electron for
(S) Minimum energy needed to remove the electron from the state
List-II
(1)
(2)
(3)
(4)
(5)
List-I
(P) Radius of the orbit with
(Q) Total energy of the electron for
(R) de Broglie wavelength of the electron for
(S) Minimum energy needed to remove the electron from the state
List-II
(1)
(2)
(3)
(4)
(5)
- A. P→4, Q→3, R→1, S→5
- B. P→4, Q→3, R→1, S→2
- C. P→1, Q→3, R→4, S→5
- D. P→4, Q→5, R→1, S→3
Show answer and solution
Answer: (A) P→4, Q→3, R→1, S→5
In the Bohr model and . (P) , which is (4). (Q) , which is (3). (R) The orbit circumference holds de Broglie wavelengths, , so , which is (1). (S) Removing the electron from needs , which is (5). The in (2) is the ground-state ionisation energy and is a distractor. All four entries follow from , and the quantisation of the orbit circumference in de Broglie wavelengths. Hence P→4, Q→3, R→1, S→5.
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