NEETPhysicsAtomic Physics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The kinetic energy of an electron in the first excited state of a hydrogen atom is four times its kinetic energy in the third excited state. Reason (R): The kinetic energy of an electron in a hydrogen atom is inversely proportional to the square of the principal quantum number. In the light of the
Options
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
- BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is not correct
- D(A) is not correct but (R) is correct
Correct answer
A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
Step-by-step solution
Reason (R) is correct: According to Bohr's model, the kinetic energy of an electron in the n^ th orbit of a hydrogen atom is K = 13.6 n^2 eV . Thus, K 1 n^2 . Assertion (A) is correct: The first excited state corresponds to the principal quantum number n₁ = 2 , and the third excited state corresponds to n₂ = 4 . Using the relation from the Reason: K₁ 1 2^2 = 1 4 K₂ 1 4^2 = 1 16 The ratio of their kinetic energies is K₁ K₂ = 1/4 1/16 = 4 . Therefore, the kinetic energy in the first excited state is four times that i