Light of two different frequencies whose photons have energies 1eV and 2.5 eV respectively illuminate a metallic surface whose work function is 0.5 eV successively. Ratio of maximum kinetic energy of emitted electrons will be:

Options

A. `1:4`
B. `1:2`
C. `1:1`
D. `1:5`

Answer

To solve the problem step by step, we need to find the maximum kinetic energy of emitted electrons for two different photon energies and then calculate the ratio of these kinetic energies.

### Step 1: Understand the Concept
The maximum kinetic energy (K.E.) of emitted electrons can be calculated using the formula:
\[ K.E. = E - \phi \]
where:
- \( E \) is the energy of the incoming photon,
- \( \phi \) is the work function of the metallic surface.

### Step 2: Identify Given Values
From the question:
- Work function \( \phi = 0.5 \, \text{eV} \)
- Energy of first photon \( E_1 = 1 \, \text{eV} \)
- Energy of second photon \( E_2 = 2.5 \, \text{eV} \)

### Step 3: Calculate Maximum Kinetic Energy for First Photon
For the first photon:
\[ K.E._{max1} = E_1 - \phi \]
\[ K.E._{max1} = 1 \, \text{eV} - 0.5 \, \text{eV} \]
\[ K.E._{max1} = 0.5 \, \text{eV} \]

### Step 4: Calculate Maximum Kinetic Energy for Second Photon
For the second photon:
\[ K.E._{max2} = E_2 - \phi \]
\[ K.E._{max2} = 2.5 \, \text{eV} - 0.5 \, \text{eV} \]
\[ K.E._{max2} = 2.0 \, \text{eV} \]

### Step 5: Calculate the Ratio of Maximum Kinetic Energies
Now, we find the ratio of the maximum kinetic energies:
\[ \text{Ratio} = \frac{K.E._{max1}}{K.E._{max2}} \]
\[ \text{Ratio} = \frac{0.5 \, \text{eV}}{2.0 \, \text{eV}} \]
\[ \text{Ratio} = \frac{1}{4} \]

### Step 6: Final Answer
Thus, the ratio of maximum kinetic energy of emitted electrons is:
\[ \text{Ratio} = 1:4 \]