A light beam of intensity `3.01xx10^(-3) W m ^(-2)` is incident normally on the square -sapped metal surface of side 1 cm and with work function 2 eV . The intensity of light is equal distributed among the three constituents' wavelength , 400 nm, 550 nm and 650 nm. Each photon emits one electron without any loss in the energy.
The energy incident by the light of wavelength 400 nm in one second is

Options

A. `1.00 xx10^(-7) J`
B. `1.07 xx10^(-7) J`
C. `1.55 xx10^(-7) J`
D. `2.00 xx10^(-7) J`

Explanation

To find the energy incident by the light of wavelength 400 nm in one second, we can follow these steps:

### Step 1: Calculate the area of the metal surface
The metal surface is square-shaped with a side of 1 cm. We need to convert this into meters for consistency with the intensity units.

\[ \text{Area} = \text{side}^2 = (1 \, \text{cm})^2 = (0.01 \, \text{m})^2 = 0.0001 \, \text{m}^2 \]

### Step 2: Determine the total energy incident on the surface in one second
The intensity of the light beam is given as \(3.01 \times 10^{-3} \, \text{W/m}^2\). The power incident on the surface can be calculated using the formula:

\[ \text{Power} = \text{Intensity} \times \text{Area} \]

Substituting the values:

\[ \text{Power} = 3.01 \times 10^{-3} \, \text{W/m}^2 \times 0.0001 \, \text{m}^2 = 3.01 \times 10^{-7} \, \text{W} \]

### Step 3: Calculate the energy incident in one second
Since power is defined as energy per unit time, the energy incident in one second is equal to the power:

\[ \text{Energy in 1 second} = \text{Power} = 3.01 \times 10^{-7} \, \text{J} \]

### Step 4: Distribute the energy among the three wavelengths
The intensity is equally distributed among the three wavelengths (400 nm, 550 nm, and 650 nm). Therefore, the energy incident due to the 400 nm wavelength can be calculated as:

\[ \text{Energy for 400 nm} = \frac{\text{Total Energy}}{3} = \frac{3.01 \times 10^{-7} \, \text{J}}{3} = 1.003 \times 10^{-7} \, \text{J} \]

### Final Answer
The energy incident by the light of wavelength 400 nm in one second is:

\[ \text{Energy} = 1.003 \times 10^{-7} \, \text{J} \]

---