AP EAMCET · Chemistry · Structure of Atom

The wavelength of the electron in the ground state of hydrogen atom is y \(Å\). What is the wavelength of the electron in the fourth orbit of \(\mathrm{He}^{+}\)ion (in \(Å\) ) is

A \(2 \mathrm{y}\)
B \(3 y\)
C \(\mathrm{y}\)
D \(\frac{3 \mathrm{y}}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3 \mathrm{y}}{2}\)

Step-by-step Solution

Detailed explanation

The wavelength of an electron in the nth energy level of a hydrogen-like atom (an atom with only one electron) is given by: \[ \lambda=h / p \] where \(h\) is Planck's constant and \(p\) is the momentum of the electron. The momentum of the electron is related to its energy and…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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