A beam of electromagnetic radiation of intensity `12.8 xx 10^(-5) W//cm^(2)` is comprised of wavelength, `lambda = 155 nm` . It falls normally on a metal (work function `phi = 2eV`) of surfacce area of the ` 1 cm^(2)`. If one in `10^(3)` photons ejects total number of electrons ejected in 1 s in `10^(x)`. (hc = 1240 eVnm) `1eV = 1.6 xx 10^(-19)`J =, then x is _____.

Explanation

To solve the problem step by step, we will follow the outlined approach in the video transcript and derive the necessary values.

### Step 1: Calculate the Energy of the Incoming Photons
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \) is Planck's constant multiplied by the speed of light (given as \( hc = 1240 \, \text{eV} \cdot \text{nm} \))
- \( \lambda \) is the wavelength in nanometers (given as \( \lambda = 155 \, \text{nm} \))

Substituting the values:
\[ E = \frac{1240 \, \text{eV} \cdot \text{nm}}{155 \, \text{nm}} = 8 \, \text{eV} \]

### Step 2: Check if the Photoelectric Effect Occurs
The work function \( \phi \) of the metal is given as \( 2 \, \text{eV} \). Since the energy of the incoming radiation \( E = 8 \, \text{eV} \) is greater than the work function \( \phi = 2 \, \text{eV} \), the photoelectric effect will occur.

### Step 3: Calculate the Power of the Incoming Radiation
The intensity \( I \) of the radiation is given as \( 12.8 \times 10^{-5} \, \text{W/cm}^2 \) and the area \( A \) is \( 1 \, \text{cm}^2 \). The power \( P \) can be calculated as:
\[ P = I \times A \]
Substituting the values:
\[ P = 12.8 \times 10^{-5} \, \text{W/cm}^2 \times 1 \, \text{cm}^2 = 12.8 \times 10^{-5} \, \text{W} \]

### Step 4: Calculate the Number of Photons per Second
The number of photons \( n \) per second can be calculated using the relationship:
\[ P = n \times E \]
Where \( E \) is the energy of one photon in joules. First, we convert \( E \) from eV to joules:
\[ E = 8 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 1.28 \times 10^{-18} \, \text{J} \]
Now, substituting the values into the power equation:
\[ 12.8 \times 10^{-5} \, \text{W} = n \times 1.28 \times 10^{-18} \, \text{J} \]
Solving for \( n \):
\[ n = \frac{12.8 \times 10^{-5}}{1.28 \times 10^{-18}} = 10^{14} \, \text{photons/s} \]

### Step 5: Calculate the Number of Electrons Ejected
Given that 1 in \( 10^3 \) photons ejects 1 electron, the number of electrons \( N \) ejected can be calculated as:
\[ N = \frac{n}{10^3} = \frac{10^{14}}{10^3} = 10^{11} \, \text{electrons/s} \]

### Step 6: Find the Value of \( x \)
The problem states that the total number of electrons ejected in 1 second is \( 10^x \). From our calculation, we found \( N = 10^{11} \). Thus, we have:
\[ x = 11 \]

### Final Answer
The value of \( x \) is \( \boxed{11} \).