Five elements `A , B , C , D` and `E` have work functions `1.2 eV , 2.4 eV , 3.6 eV , 4.8 eV` and `6 eV` respectively . If light of wavelength `4000 Å` is allowed to fall on these elements , then photoelectrons are emitted by

Options

A. A,B and C
B. A,B,C,D and E
C. A and B
D. Only E

Answer

To solve the problem step by step, we will follow these procedures:

### Step 1: Convert Wavelength to Meters
The given wavelength is \( 4000 \, \text{Å} \). We need to convert this into meters.

\[ \text{Wavelength} \, (\lambda) = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} \]

### Step 2: Calculate the Energy of Incident Light
Using the formula for the energy of a photon:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( h = 6.63 \times 10^{-34} \, \text{Js} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 4000 \times 10^{-10} \, \text{m} \)

Substituting the values:

\[ E = \frac{(6.63 \times 10^{-34}) \times (3 \times 10^8)}{4000 \times 10^{-10}} \]

Calculating this gives:

\[ E \approx 4.95 \times 10^{-19} \, \text{J} \]

### Step 3: Convert Energy from Joules to Electron Volts
To convert the energy from Joules to electron volts, we use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):

\[ E \, (\text{in eV}) = \frac{4.95 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 3.09 \, \text{eV} \]

### Step 4: Compare Energy with Work Functions
Now we compare the calculated energy \( 3.09 \, \text{eV} \) with the work functions of the elements:

- Element A: \( 1.2 \, \text{eV} \) (E > 1.2 eV)
- Element B: \( 2.4 \, \text{eV} \) (E > 2.4 eV)
- Element C: \( 3.6 \, \text{eV} \) (E < 3.6 eV)
- Element D: \( 4.8 \, \text{eV} \) (E < 4.8 eV)
- Element E: \( 6 \, \text{eV} \) (E < 6 eV)

### Step 5: Determine Which Elements Emit Photoelectrons
Photoelectrons will be emitted by elements where the energy of the incident light is greater than the work function:

- Elements A and B have work functions less than \( 3.09 \, \text{eV} \), so they will emit photoelectrons.
- Elements C, D, and E have work functions greater than \( 3.09 \, \text{eV} \), so they will not emit photoelectrons.

### Final Answer
Photoelectrons are emitted by elements **A and B**.

---