If light of wavelength 6200Å falls on a photosensitive surface of work function 2 eV, the kinetic energy of the most energetic photoelectron will be

Options

A. 0.5 eV
B. 1 eV
C. zero
D. 0.75 eV

Explanation

To solve the problem of finding the kinetic energy of the most energetic photoelectron when light of wavelength 6200 Å falls on a photosensitive surface with a work function of 2 eV, we can follow these steps:

### Step 1: Convert the wavelength from Angstroms to meters
The wavelength is given as 6200 Å. We need to convert this to meters for further calculations:
\[ \text{Wavelength} (\lambda) = 6200 \, \text{Å} = 6200 \times 10^{-10} \, \text{m} \]

### Step 2: Calculate the energy of the incident photons
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( c \) (speed of light) = \( 3 \times 10^8 \, \text{m/s} \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{6200 \times 10^{-10} \, \text{m}} \]

### Step 3: Calculate the energy in electron volts
To convert the energy from joules to electron volts, we use the conversion factor \( 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \):
\[ E \, (\text{in eV}) = \frac{E \, (\text{in J})}{1.602 \times 10^{-19}} \]

### Step 4: Calculate the kinetic energy of the photoelectron
The kinetic energy (KE) of the most energetic photoelectron can be calculated using the photoelectric equation:
\[ KE = E - W \]
where \( W \) is the work function. Given that \( W = 2 \, \text{eV} \):
\[ KE = E - 2 \, \text{eV} \]

### Step 5: Substitute the values and calculate
After calculating \( E \) in eV from the previous steps, we can substitute it into the kinetic energy equation to find the final result.

### Final Calculation
1. Calculate \( E \) using the values provided.
2. Substitute \( E \) into the kinetic energy equation to find \( KE \).

### Conclusion
If the calculated energy \( E \) is equal to the work function \( W \), then:
\[ KE = E - W = 0 \, \text{eV} \]