Energy required to stop the ejection of electrons from certain metal plate was found to be 0.2 eV when an electromagnetic radiation of 330 nm was made to fall on it the work function of the metal is

Options

A. `0.32 xx10^(-19)` j
B. `6xx10^(-19) j`
C. `5.68 xx10^(-19)` j
D. `3.82 xx10^(-27)`

Answer

To find the work function of the metal, we can use the photoelectric effect equation:

\[ E = \frac{hc}{\lambda} - \phi \]

where:
- \( E \) is the energy of the incident photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the incident light (in meters),
- \( \phi \) is the work function of the metal.

### Step 1: Convert the wavelength from nanometers to meters
Given that the wavelength \( \lambda = 330 \, \text{nm} \):

\[ \lambda = 330 \, \text{nm} = 330 \times 10^{-9} \, \text{m} \]

### Step 2: Calculate the energy of the incident photon \( E \)
Using the formula \( E = \frac{hc}{\lambda} \):

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{330 \times 10^{-9} \, \text{m}} \]

Calculating this gives:

\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{330 \times 10^{-9} \, \text{m}} = 6.023 \times 10^{-19} \, \text{J} \]

### Step 3: Convert the stopping energy from eV to Joules
Given that the energy required to stop the ejection of electrons is \( 0.2 \, \text{eV} \):

\[ 0.2 \, \text{eV} = 0.2 \times 1.6 \times 10^{-19} \, \text{J} = 0.32 \times 10^{-19} \, \text{J} \]

### Step 4: Use the photoelectric effect equation to find the work function \( \phi \)
Rearranging the equation:

\[ \phi = E - 0.2 \, \text{eV} \]

Substituting the values:

\[ \phi = 6.023 \times 10^{-19} \, \text{J} - 0.32 \times 10^{-19} \, \text{J} \]

Calculating this gives:

\[ \phi = 5.703 \times 10^{-19} \, \text{J} \]

### Step 5: Convert the work function back to eV (if needed)
To convert back to eV:

\[ \phi = \frac{5.703 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 3.56 \, \text{eV} \]

### Final Answer:
The work function of the metal is approximately \( 3.56 \, \text{eV} \).

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