If Photon having wavelength `6.2nm`was allowed to strike a metal plate having work function `50eV` then calculate wavelength associated with emitted electron `:`

Options

A. `1xx10^(-10)m`
B. `2xx10^(-10)m`
C. `3xx10^(-18)m`
D. `4xx10^(-34)m`

Explanation

To solve the problem of calculating the wavelength associated with the emitted electron when a photon of wavelength 6.2 nm strikes a metal plate with a work function of 50 eV, we can follow these steps:

### Step 1: Calculate the Energy of the Incident Photon
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength of the photon.

Given that the wavelength \(\lambda = 6.2 \, \text{nm} = 6.2 \times 10^{-9} \, \text{m}\), we can substitute the values into the equation.

### Step 2: Substitute Values and Calculate Energy
Substituting the values into the formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3.00 \times 10^8 \, \text{m/s})}{6.2 \times 10^{-9} \, \text{m}} \]

Calculating this gives:
\[ E \approx \frac{1.9878 \times 10^{-25}}{6.2 \times 10^{-9}} \approx 3.20 \times 10^{-18} \, \text{J} \]

To convert this energy into electron volts (eV), we use the conversion factor \(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}\):
\[ E \approx \frac{3.20 \times 10^{-18} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 20 \, \text{eV} \]

### Step 3: Calculate the Kinetic Energy of the Emitted Electron
The kinetic energy (KE) of the emitted electron can be calculated using the formula:
\[ KE = E - \text{Work Function} \]
Given that the work function is 50 eV:
\[ KE = 20 \, \text{eV} - 50 \, \text{eV} = -30 \, \text{eV} \]

Since the kinetic energy cannot be negative, this indicates that the photon does not have enough energy to overcome the work function of the metal, and thus no electrons are emitted.

### Step 4: Conclusion
Since no electrons are emitted due to insufficient energy, we cannot calculate a wavelength associated with emitted electrons.