Photoelectron are liberated by altra voilet light of wavelength `3000Å`from a metallic surface for which the photoelectron thershold is `4000 Å` calculate de broglic wavelength of electron with maximum kinetic energy

Explanation

To solve the problem, we need to calculate the de Broglie wavelength of the electron with maximum kinetic energy after being liberated by ultraviolet light. Here’s a step-by-step solution:

### Step 1: Understand the given data
- Wavelength of ultraviolet light, \( \lambda = 3000 \, \text{Å} = 3000 \times 10^{-10} \, \text{m} \)
- Threshold wavelength, \( \lambda_{\text{th}} = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} \)

### Step 2: Calculate the energy of the incident photon
Using the formula for the energy of a photon:
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