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NEET CHEMISTRYMedium

Given below are two statements: Statement I: The energy of the He⁺ ion in n=2 state is same as the energy of H atom in n=1 state. Statement II: It is possible to determine simultaneously the exact position and exact momentum of an electron in H atom.

In light of the above statements, choose the correct answer from the options given below:

A

Both Statement I and Statement II are true

B

Both Statement I and Statement II are false

C

Statement I is true and Statement II is false

D

Statement I is false, and Statement II is true

Step-by-Step Solution

  1. Analyze Statement I: According to Bohr's theory, the energy of an electron in the n-th orbit of a hydrogen-like species is given by En∝Z2n2E_n \propto \frac{Z^2}{n^2}. For Hydrogen atom (H): Z=1Z=1, n=1n=1. Thus, E1(H)∝1212=1E_1(H) \propto \frac{1^2}{1^2} = 1. For Helium ion (He+He^+): Z=2Z=2, n=2n=2. Thus, E2(He+)∝2222=1E_2(He^+) \propto \frac{2^2}{2^2} = 1.
  • Since the ratios are identical, the energies are the same (E=−2.18×10−18 JE = -2.18 \times 10^{-18} \text{ J}). Therefore, Statement I is True .
  1. Analyze Statement II: According to Heisenberg's Uncertainty Principle, it is impossible to determine simultaneously the exact position and exact momentum (or velocity) of a microscopic particle like an electron . Therefore, Statement II is False.

Conclusion: Statement I is true and Statement II is false.

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