On a photosensitive metal of area`1 cm^(2)` and work function 2eV, light of intensity `6.4 xx 10^(–5) W//cm^(2)` in wavelength 310 nm fall normally. If 1 out of every `10^(3)` photons are successful, then number of photoelectrons emitted in one second is 10x. Find x

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the Power of the Light
The power \( P \) of the light incident on the photosensitive metal can be calculated using the formula:
\[ P = \text{Intensity} \times \text{Area} \]
Given:
- Intensity \( = 6.4 \times 10^{-5} \, \text{W/cm}^2 \)
- Area \( = 1 \, \text{cm}^2 \)

Substituting the values:
\[ P = 6.4 \times 10^{-5} \, \text{W/cm}^2 \times 1 \, \text{cm}^2 = 6.4 \times 10^{-5} \, \text{W} \]

### Step 2: Calculate the Energy of One Photon
The energy \( E \) of one photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \) (Planck's constant) \( = 4.1357 \times 10^{-15} \, \text{eV s} \)
- \( c \) (speed of light) \( = 3 \times 10^8 \, \text{m/s} \)
- \( \lambda = 310 \, \text{nm} = 310 \times 10^{-9} \, \text{m} \)

Using the value of \( hc \) in eV·nm, we have:
\[ hc = 1240 \, \text{eV·nm} \]
Thus,
\[ E = \frac{1240 \, \text{eV·nm}}{310 \, \text{nm}} = 4 \, \text{eV} \]

### Step 3: Convert Energy of One Photon to Joules
To convert the energy from eV to Joules, we use:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Thus,
\[ E = 4 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 6.4 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the Number of Photons Emitted per Second
The number of photons \( n \) emitted per second can be calculated using:
\[ n = \frac{P}{E} \]
Substituting the values:
\[ n = \frac{6.4 \times 10^{-5} \, \text{W}}{6.4 \times 10^{-19} \, \text{J}} = 10^{14} \, \text{photons/second} \]

### Step 5: Calculate the Number of Successful Photoelectrons
Given that 1 out of every 1000 photons is successful, the number of successful photoelectrons emitted per second is:
\[ \text{Successful photoelectrons} = \frac{n}{1000} = \frac{10^{14}}{1000} = 10^{11} \]

### Step 6: Find the Value of \( x \)
The problem states that the number of photoelectrons emitted in one second is \( 10x \). Therefore, we can equate:
\[ 10x = 10^{11} \]
From this, we can find \( x \):
\[ x = 10^{10} \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{11} \]