AP EAMCET · Chemistry · Structure of Atom

If, the binding energy of electrons in a metal is \(250 \mathrm{~kJ} / \mathrm{mol}\), what should be the threshold frequency of the striking photons in order to free an electron from the metal surface?

A \(6.26 \times 10^{14} \mathrm{~s}^{-1}\)
B \(12.4 \times 10^{14} \mathrm{~s}^{-1}\)
C \(6.26 \times 10^{12} \mathrm{~s}^{-1}\)
D \(12.4 \times 10^{12} \mathrm{~s}^{-1}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(6.26 \times 10^{14} \mathrm{~s}^{-1}\)

Step-by-step Solution

Detailed explanation

Binding energy of 1 mole of electrons \(=250 \mathrm{~kJ}\) Binding energy of 1 electron \(\begin{aligned} & =(250) /\left(6.022 \times 10^{23}\right) \mathrm{kJ} \\ & =4.15 \times 10^{-22} \mathrm{~kJ} \\ & =4.15 \times 10^{-19} \mathrm{~J} \end{aligned}\) Threshold energy…

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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