The photoelectric threshold wavelength of silver is `3250 xx 10^(-10) m`. The velocity of the electron ejected from a silver surface by ultraviolet light of wavelength `2536 xx 10^(-10) m` is
`(Given h = 4.14 xx 10^(6) ms^(-1) eVs` and `c = 3 xx 10^(8) ms^(-1))`

Options

A. `~~ 6 xx 10^(5) ms^(-1)`
B. `~~ 0.6 xx 10^(6) ms^(-1)`
C. `~~ 61 xx 10^(3) ms_(-1)`
D. `~~ 0.3 xx 10^(6) ms^(-1)`

Answer

To solve the problem of finding the velocity of the electron ejected from a silver surface by ultraviolet light, we will follow these steps:

### Step 1: Identify the given values
- Threshold wavelength of silver, \( \lambda_0 = 3250 \times 10^{-10} \, m \)
- Wavelength of incident ultraviolet light, \( \lambda = 2536 \times 10^{-10} \, m \)
- Planck's constant, \( h = 4.14 \times 10^{-6} \, ms^{-1} \, eVs \)
- Speed of light, \( c = 3 \times 10^{8} \, ms^{-1} \)

### Step 2: Calculate the energy of the incident light
The energy \( E \) of the incident light can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Substituting the values:
\[ E = \frac{(4.14 \times 10^{-6} \, ms^{-1} \, eVs) \times (3 \times 10^{8} \, ms^{-1})}{2536 \times 10^{-10} \, m} \]

### Step 3: Calculate the work function (φ)
The work function \( \phi \) can be calculated using the threshold wavelength:
\[ \phi = \frac{hc}{\lambda_0} \]
Substituting the values:
\[ \phi = \frac{(4.14 \times 10^{-6} \, ms^{-1} \, eVs) \times (3 \times 10^{8} \, ms^{-1})}{3250 \times 10^{-10} \, m} \]

### Step 4: Calculate the kinetic energy (KE) of the ejected electron
The kinetic energy \( KE \) of the ejected electron is given by:
\[ KE = E - \phi \]

### Step 5: Calculate the velocity of the electron
The kinetic energy can also be expressed in terms of the velocity \( v \) of the electron:
\[ KE = \frac{1}{2} mv^2 \]
Where \( m \) is the mass of the electron, \( m = 9.1 \times 10^{-31} \, kg \). Rearranging gives:
\[ v = \sqrt{\frac{2 \cdot KE}{m}} \]

### Step 6: Substitute and calculate the final velocity
Now we can substitute the values of \( KE \) and \( m \) into the equation to find \( v \).

### Final Calculation
1. Calculate \( E \) and \( \phi \) using the formulas from Steps 2 and 3.
2. Calculate \( KE \) from Step 4.
3. Finally, calculate \( v \) from Step 5.