Photon of wavelength 400nm strikes on a material with energy 1000J in 10secs. What will be no. of electron leaving the material in one second?

Options

A. `5×10^9`
B. `5 ×10^16`
C. `5×10^13`
D. `5×10^10`

Answer

To solve the problem, we need to find the number of electrons leaving the material in one second when a photon of wavelength 400 nm strikes it, given that the total energy delivered is 1000 J in 10 seconds.

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
The wavelength (λ) is given as 400 nm. We need to convert this to meters.
\[ \lambda = 400 \, \text{nm} = 400 \times 10^{-9} \, \text{m} \]

**Hint**: Remember that 1 nm = \(10^{-9}\) m.

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

Plugging in the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{400 \times 10^{-9} \, \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{400 \times 10^{-9}} = 4.9695 \times 10^{-19} \, \text{J} \]

**Hint**: Use the formula for photon energy and ensure units are consistent.

3. **Calculate the Total Energy Delivered in One Second**:
The total energy delivered in 10 seconds is 1000 J. Therefore, the energy delivered in one second is:
\[ E_{\text{one second}} = \frac{1000 \, \text{J}}{10 \, \text{s}} = 100 \, \text{J} \]

**Hint**: Divide the total energy by the time to find the energy per second.

4. **Calculate the Number of Photons Striking the Material in One Second**:
To find the number of photons (N) striking the material in one second, we use:
\[ N = \frac{E_{\text{one second}}}{E} \]
Substituting the values:
\[ N = \frac{100 \, \text{J}}{4.9695 \times 10^{-19} \, \text{J}} \approx 2.01 \times 10^{20} \]

**Hint**: This gives the total number of photons striking the material in one second.

5. **Determine the Number of Electrons Leaving the Material**:
Assuming each photon can release one electron, the number of electrons leaving the material in one second is equal to the number of photons:
\[ \text{Number of electrons} = N \approx 2.01 \times 10^{20} \]

**Hint**: In the photoelectric effect, one photon can typically release one electron.

### Final Answer:
The number of electrons leaving the material in one second is approximately \(2.01 \times 10^{20}\).