All electrons ejected from a surface by incident light of wavelength 200nm can be stopped before traveling 1m in the direction of a uniform electric field of `4 NC^(-1)`. The work function of the surface is

Options

A. 4eV
B. 6.2 eV
C. 2 eV
D. 2.2 eV

Explanation

To solve the problem, we need to find the work function of the surface from which electrons are ejected when exposed to light of a given wavelength. Here are the steps to arrive at the solution:

### Step 1: Calculate the energy of the incident light
The energy of the incident light can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h = 6.626 \times 10^{-34} \, \text{Js} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 200 \, \text{nm} = 200 \times 10^{-9} \, \text{m} \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34})(3 \times 10^8)}{200 \times 10^{-9}} \]
Calculating this gives:
\[ E \approx 9.9 \times 10^{-19} \, \text{J} \]

### Step 2: Convert the energy from Joules to electron volts
To convert energy from Joules to electron volts, we use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E \, (\text{in eV}) = \frac{9.9 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 6.19 \, \text{eV} \]

### Step 3: Determine the stopping potential
The stopping potential \( V_0 \) can be calculated using the formula:
\[ V_0 = E \cdot d \]
where:
- \( E = 4 \, \text{N/C} \) (electric field strength)
- \( d = 1 \, \text{m} \) (distance)

Thus:
\[ V_0 = 4 \times 1 = 4 \, \text{V} \]

### Step 4: Calculate the maximum kinetic energy of the ejected electrons
The maximum kinetic energy \( KE \) of the ejected electrons is given by:
\[ KE = e \cdot V_0 \]
where \( e = 1.6 \times 10^{-19} \, \text{C} \) (charge of an electron). Therefore:
\[ KE = 1.6 \times 10^{-19} \times 4 \approx 6.4 \times 10^{-19} \, \text{J} \]
Converting this to electron volts:
\[ KE \, (\text{in eV}) = \frac{6.4 \times 10^{-19}}{1.6 \times 10^{-19}} = 4 \, \text{eV} \]

### Step 5: Use Einstein's photoelectric equation to find the work function
Einstein's photoelectric equation is given by:
\[ KE = E - \phi \]
where \( \phi \) is the work function. Rearranging gives:
\[ \phi = E - KE \]
Substituting the values we found:
\[ \phi = 6.19 \, \text{eV} - 4 \, \text{eV} = 2.19 \, \text{eV} \]

### Conclusion
The work function of the surface is approximately \( 2.19 \, \text{eV} \).