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The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 are
- a)n1 = 4, n2 = 2
- b)n1 = 8, n2 = 2
- c)n1 = 4, n2 = 1
- d)n1 = 6, n2 = 3
Correct answer is option 'A,D'. Can you explain this answer?
Most Upvoted Answer
The electron in a hydrogen atom makes a transition n1 → n2, where n1 ...
**Bohr’s Model of Hydrogen Atom**
Bohr’s model of hydrogen atom states that the electron moves in circular orbits around the nucleus. Each orbit is associated with a certain energy level, which is quantized, and is given by the principal quantum number, n.
**Time period of electron in an orbit**
The time period of an electron in an orbit is given by the equation:
T = 2πr/v
Where r is the radius of the orbit and v is the velocity of the electron.
**Transition n1 → n2**
When an electron moves from an initial state with principal quantum number n1 to a final state with principal quantum number n2, it is said to make a transition n1 → n2. During this transition, the electron emits or absorbs a photon with energy equal to the difference in energy between the two states.
**Given**
The time period of the electron in the initial state is eight times that in the final state.
T1 = 8T2
**Solution**
Let us assume that the electron makes a transition n1 → n2.
From Bohr’s model, we know that the radius of the nth orbit is given by the equation:
rn = n²h²/4π²me²
where h is Planck’s constant, m is the mass of the electron, and e is the charge of the electron.
Also, we know that the velocity of the electron in the nth orbit is given by:
vn = e²/2nh
Using these equations, we can write the time period of the electron in the nth orbit as:
Tn = 2πrn/vn = 4π²me²n³/h³e⁴
Let us assume that n2 < n1.="" then,="" using="" the="" given="" equation="" t1="8T2," we="" />
4π²me²n1³/h³e⁴ = 8(4π²me²n2³/h³e⁴)
Simplifying and solving for n1 and n2, we get:
n1 = 4n2
Hence, the possible values of n1 and n2 are:
a) n1 = 4, n2 = 2
d) n1 = 6, n2 = 3
Therefore, options A and D are correct.
Bohr’s model of hydrogen atom states that the electron moves in circular orbits around the nucleus. Each orbit is associated with a certain energy level, which is quantized, and is given by the principal quantum number, n.
**Time period of electron in an orbit**
The time period of an electron in an orbit is given by the equation:
T = 2πr/v
Where r is the radius of the orbit and v is the velocity of the electron.
**Transition n1 → n2**
When an electron moves from an initial state with principal quantum number n1 to a final state with principal quantum number n2, it is said to make a transition n1 → n2. During this transition, the electron emits or absorbs a photon with energy equal to the difference in energy between the two states.
**Given**
The time period of the electron in the initial state is eight times that in the final state.
T1 = 8T2
**Solution**
Let us assume that the electron makes a transition n1 → n2.
From Bohr’s model, we know that the radius of the nth orbit is given by the equation:
rn = n²h²/4π²me²
where h is Planck’s constant, m is the mass of the electron, and e is the charge of the electron.
Also, we know that the velocity of the electron in the nth orbit is given by:
vn = e²/2nh
Using these equations, we can write the time period of the electron in the nth orbit as:
Tn = 2πrn/vn = 4π²me²n³/h³e⁴
Let us assume that n2 < n1.="" then,="" using="" the="" given="" equation="" t1="8T2," we="" />
4π²me²n1³/h³e⁴ = 8(4π²me²n2³/h³e⁴)
Simplifying and solving for n1 and n2, we get:
n1 = 4n2
Hence, the possible values of n1 and n2 are:
a) n1 = 4, n2 = 2
d) n1 = 6, n2 = 3
Therefore, options A and D are correct.
Community Answer
The electron in a hydrogen atom makes a transition n1 → n2, where n1 ...
Time period, (in nth state)
i.e. 
But rn ∝ n2 and vn ∝ 1 / n
Therefore, Tn ∝ n3
Given
Hence, n1 = 2n2
Option that satisfy above condition are
( n1 = 4, n2 = 2 and n1 = 6, n2 = 3 )
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The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer?
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The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer?.
The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The electron in a hydrogen atom makes a transition n1 → n2, where n1 and n2 are the principal quantum numbers of two states. Assume the Bohr’s 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 and n2 area)n1 = 4, n2 = 2b)n1 = 8, n2 = 2c)n1 = 4, n2 = 1d)n1 = 6, n2 = 3Correct answer is option 'A,D'. Can you explain this answer?.
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