The work function of a certain metal is `3.31xx10^(-19) j`then, the maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength `5000`Å IS(GIVEN,h=`6.62XX10^(-34)J_(-s),c=3xx10^(8)ms^(-1),e=1.6xx10^(-19)C)`

Options

A. 2.48 eV
B. 0.41 eV
C. 2.07 eV
D. 0.82 eV

Answer

To find the maximum kinetic energy of photoelectrons emitted by incident radiation of wavelength \(5000 \, \text{Å}\) (or \(5000 \times 10^{-10} \, \text{m}\)), we can follow these steps:

### Step-by-Step Solution:

1. **Convert Wavelength to Meters:**
\[ \text{Wavelength} (\lambda) = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-7} \, \text{m} \]

2. **Calculate the Energy of the Incident Photon:**
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h = 6.62 \times 10^{-34} \, \text{J s}\) (Planck's constant)
- \(c = 3 \times 10^{8} \, \text{m/s}\) (speed of light)

Substituting the values:
\[ E = \frac{(6.62 \times 10^{-34} \, \text{J s})(3 \times 10^{8} \, \text{m/s})}{5.0 \times 10^{-7} \, \text{m}} \]
\[ E = \frac{1.986 \times 10^{-25} \, \text{J m}}{5.0 \times 10^{-7} \, \text{m}} = 3.972 \times 10^{-19} \, \text{J} \]

3. **Convert the Work Function to Electron Volts:**
The work function \(W\) is given as \(3.31 \times 10^{-19} \, \text{J}\). To convert this to electron volts:
\[ W = \frac{3.31 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 2.06875 \, \text{eV} \]

4. **Calculate the Maximum Kinetic Energy of the Photoelectrons:**
The maximum kinetic energy \(K.E.\) of the emitted photoelectrons can be calculated using the formula:
\[ K.E. = E - W \]
Substituting the values:
\[ K.E. = (3.972 \times 10^{-19} \, \text{J}) - (3.31 \times 10^{-19} \, \text{J}) = 6.62 \times 10^{-20} \, \text{J} \]

5. **Convert Kinetic Energy to Electron Volts:**
\[ K.E. = \frac{6.62 \times 10^{-20} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 0.41375 \, \text{eV} \]

### Final Answer:
The maximum kinetic energy of the photoelectrons emitted is approximately \(0.41 \, \text{eV}\).

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