AP EAMCET · Chemistry · Structure of Atom

Which of the following equations represents the velocity $(v)$ of the ejected electrons when a metal is made to strike with light of frequency $v$ and the threshold frequency of the metal is $v_{0} ?$ $(m_{e} =$ mass of electron and $h$ is Planck's constant).

A $v = \sqrt{\frac{h (v - v_{0})}{m_{e}}}$
B $v = \sqrt{\frac{2 h (v - v_{0})}{m_{e}}}$
C $v = \sqrt{\frac{h (v - v_{0})}{2 m_{e}}}$
D $v = \sqrt{h (v - v_{0}) m_{e}}$

Verified Solution

Answer & Solution

Correct Answer

(B) $v = \sqrt{\frac{2 h (v - v_{0})}{m_{e}}}$

Step-by-step Solution

Detailed explanation

As in case of photoelectric effect, incident radiation energy is equal to the sum of threshold energy and kinetic energy. hv=hv0 + 12mev2v2=2h(v-v0)mev=2h(v-v0)me

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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Which of the following equations represents the velocity (v) of the ejected electrons when a metal is made to strike with light of frequency v and the threshold frequency of the metal is v0? me=mass of electron and h is Planck's constant).

Step-by-step Solution

Which of the following equations represents the velocity $(v)$ of the ejected electrons when a metal is made to strike with light of frequency $v$ and the threshold frequency of the metal is $v_{0} ?$ $(m_{e} =$ mass of electron and $h$ is Planck's constant).