TS EAMCET · Chemistry · Structure of Atom

Wavelength of \(\mathrm{H}^{+}\)ion with kinetic energy \(1.65 \mathrm{eV}\) is \(\left(\right.\) mass of proton \(=1.6726 \times 10^{-27} \mathrm{~kg}\) )

A \(1.22 \mathrm{~nm}\)
B \(0.22 \mathrm{~nm}\)
C 0.022 nm
D \(0.122 \mathrm{~nm}\)

Verified Solution

Answer & Solution

Correct Answer

(C) 0.022 nm

Step-by-step Solution

Detailed explanation

Given, kinetic energy of \(\mathrm{H}^{+}\)ion \(=1.68 \mathrm{eV}\) Mass of proton \(=1.6726 \times 10^{-27} \mathrm{~kg}\) We calculate, the wavelength of \(\mathrm{H}^{+}\)ion as follows: \(\lambda=\frac{h}{\sqrt{2 E_m}}\) Here, \(E=\) kinetic energy, \(m=\) mass of proton…

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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