The work function of a metal is 4 eV if 5000 Å wavelength of light is incident on the metal. Is there any photo electric effect ?

Answer

To determine whether there is a photoelectric effect when light of a certain wavelength strikes a metal, we need to compare the energy of the incident photons with the work function of the metal. Here’s a step-by-step solution:

### Step 1: Understand the Work Function
The work function (Φ) of a metal is the minimum energy required to remove an electron from the surface of that metal. In this case, the work function is given as 4 eV.

### Step 2: Calculate the Energy of the Incident Light
The energy (E) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \) is Planck's constant (\( 4.1357 \times 10^{-15} \) eV·s),
- \( c \) is the speed of light (\( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength of the light in meters.

Since the wavelength is given in angstroms (Å), we convert it to meters:
\[ 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

Now, substituting the values into the energy formula:
\[ E = \frac{(4.1357 \times 10^{-15} \, \text{eV·s}) \times (3 \times 10^8 \, \text{m/s})}{5 \times 10^{-7} \, \text{m}} \]

### Step 3: Simplify the Calculation
Calculating the energy:
\[ E = \frac{(4.1357 \times 3) \times 10^{-7} \, \text{eV·m}}{5} \]
\[ E = \frac{12.4071 \times 10^{-7}}{5} \]
\[ E = 2.48142 \, \text{eV} \]

### Step 4: Compare the Energy with the Work Function
Now, we compare the calculated energy of the incident light with the work function:
- Energy of incident light = 2.48 eV
- Work function = 4 eV

Since \( 2.48 \, \text{eV} < 4 \, \text{eV} \), the energy of the incident light is less than the work function of the metal.

### Step 5: Conclusion
Because the energy of the incident photons is less than the work function, no electrons will be emitted from the metal surface. Therefore, there will be no photoelectric effect.

### Final Answer
**No, there is no photoelectric effect.**

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