It takes 4.6 eV remove one of the least tightly bound electrons from a metal surface . When monochromatic photons strike energy from zero to 2.2 eV are ejected . What is the energy of the incident photons ?

Options

A. 2.4 eV
B. 2.2 eV
C. 6.8 eV
D. 4.6 eV

Answer

To solve the problem step by step, we will follow the concepts of the photoelectric effect and the relationship between work function, incident photon energy, and kinetic energy of ejected electrons.

### Step 1: Understand the Work Function
The work function (φ) is the minimum energy required to remove an electron from the surface of a metal. In this case, it is given as:
\[ \phi = 4.6 \, \text{eV} \]

### Step 2: Identify the Maximum Kinetic Energy of Ejected Electrons
The problem states that when monochromatic photons strike the metal, electrons with kinetic energy ranging from 0 to 2.2 eV are ejected. Therefore, the maximum kinetic energy (K.E.) of the ejected electrons is:
\[ K.E. = 2.2 \, \text{eV} \]

### Step 3: Apply the Photoelectric Equation
According to the photoelectric effect, the energy of the incident photon (E) can be expressed as:
\[ E = \phi + K.E. \]
Where:
- \(E\) is the energy of the incident photon,
- \(\phi\) is the work function,
- \(K.E.\) is the kinetic energy of the ejected electron.

### Step 4: Substitute the Known Values
Now, we can substitute the known values into the equation:
\[ E = 4.6 \, \text{eV} + 2.2 \, \text{eV} \]

### Step 5: Calculate the Energy of the Incident Photon
Now, we perform the addition:
\[ E = 4.6 \, \text{eV} + 2.2 \, \text{eV} = 6.8 \, \text{eV} \]

### Conclusion
The energy of the incident photons is:
\[ E = 6.8 \, \text{eV} \]

### Final Answer
Thus, the energy of the incident photons is 6.8 eV.

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