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Question #41994
The Question
In a non-linear model of the photoelectric effect, the intense incident light modifies the surface properties of a metal. The maximum kinetic energy of the emitted photoelectrons is given by the relation: where is Planck's constant, is the frequency of the incident light, is its wavelength in vacuum, is the intensity of the incident light, is the baseline work function of the material, and is a positive constant. Assuming the equation is dimensionally consistent, what is the dimensional formula of the constant , and what is the theoretical threshold frequency in the limit of extremely high light intensity ()?
Options
- A.
and
- B.
and
- C.
and
- D.
and
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Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Intuition_Breaker
Train your brain to resist "obvious" answers that are designed to deceive your intuition.
Concepts Behind This Question
Dimensional Consistency and Transcendental Functions|Einstein's Photoelectric Equation|Work Function Dependence
Why This Question Is Tricky
Common Mistakes
This question tests the student's ability to synthesize dimensional analysis with limiting cases in a modified physical model.
The 'Lethal Collision' occurs when students correctly determine the dimensions of but blindly rely on rote memory for the threshold frequency ().
They fail to recognize that the work function is a dynamic variable dependent on intensity.
By taking the limit , the effective work function exponentially decays to zero, fundamentally altering the threshold condition to .
This penalizes the assumption that standard textbook formulas apply universally without analyzing the specific mathematical model provided.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Units and Measurements - Class 11 Part 1 |
| Concept | Dimensional Consistency and Transcendental Functions |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |