Q26. In a hydrogen atom an electron makes a transition from n₁ → n₂, where n₁ and n₂ are the princip

Q: What is the correct answer for CUET UG Physics Q26?

The correct answer is a. According to Bohr's model for the hydrogen atom, the time period (T) of an electron in a particular orbit is directly proportional to the cube of its principal quantum number (n). That is, T ∝ n³. Given that the time period of the electron in the initial state (T₁) is eight times that in the final state (T₂), we have T₁ = 8T₂. Using the proportionality, we can write the ratio of time periods as T₁

Q: Q26. In a hydrogen atom an electron makes a transition from n₁ → n₂, where n₁ and n₂ are the principal quantum numbers of these two states. Assuming Bohr's model to be valid, if the time period of…

The correct answer is a. According to Bohr's model for the hydrogen atom, the time period (T) of an electron in a particular orbit is directly proportional to the cube of its principal quantum number (n). That is, T ∝ n³. Given that the time period of the electron in the initial state (T₁) is eight times that in the final state (T₂), we have T₁ = 8T₂. Using the proportionality, we can write the ratio of time periods as T₁

Q: What are the options for this CUET UG Physics question?

A. n₁ = 8, n₂ = 4 · B. n₁ = 4, n₂ = 8 · C. n₁ = 8, n₂ = 2 · D. n₁ = 2, n₂ = 8

Question

Q26. In a hydrogen atom an electron makes a transition from n₁ → n₂, where n₁ and n₂ are the principal quantum numbers of these two states. Assuming Bohr's model to be valid, if the time period of electron in the initial state is eight times of that in the final state, the possible values of n₁ and n₂ are:
(a) n₁ = 8, n₂ = 4
(b) n₁ = 4, n₂ = 8
(c) n₁ = 8, n₂ = 2
(d) n₁ = 2, n₂ = 8

FirstInTest · Accepted Answer

According to Bohr's model for the hydrogen atom, the time period (T) of an electron in a particular orbit is directly proportional to the cube of its principal quantum number (n). That is, T ∝ n³. Given that the time period of the electron in the initial state (T₁) is eight times that in the final state (T₂), we have T₁ = 8T₂. Using the proportionality, we can write the ratio of time periods as T₁/T₂ = (n₁/n₂)³. Substituting the given condition: 8T₂/T₂ = (n₁/n₂)³, which simplifies to 8 = (n₁/n₂)³. Taking the cube root of both sides, we get 2 = n₁/n₂, or n₁ = 2n₂. Now, we check the given options to find which pair satisfies this relationship: (a) n₁ = 8, n₂ = 4: 8 = 2 × 4, which is correct. The other options do not satisfy this relation.

Answer

n₁ = 8, n₂ = 4

Answer

n₁ = 4, n₂ = 8

Answer

n₁ = 8, n₂ = 2

Answer

n₁ = 2, n₂ = 8

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