Four elements A, B, C, D have work function 2, 2.4, 2.8, 3.2 eV. Light of wavelength 4000 Å is incident on them. The elements which emit photo electrons are

Options

A. A, B, C, D
B. A, B, C
C. A, B
D. A

Answer

To solve the problem, we need to determine which of the four elements (A, B, C, D) will emit photoelectrons when exposed to light of a specific wavelength. The key concept here is the photoelectric effect, which states that electrons are emitted from a material when the energy of the incident light is greater than the work function of that material.

### Step-by-Step Solution:

1. **Identify the Work Functions**:
- The work functions for the elements are given as:
- A: 2 eV
- B: 2.4 eV
- C: 2.8 eV
- D: 3.2 eV

2. **Calculate the Energy of the Incident Light**:
- The energy of the incident light can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
- Where:
- \( h \) (Planck's constant) = \( 6.63 \times 10^{-34} \, \text{Js} \)
- \( c \) (speed of light) = \( 3 \times 10^8 \, \text{m/s} \)
- \( \lambda \) (wavelength) = 4000 Å = \( 4000 \times 10^{-10} \, \text{m} \)

3. **Convert Wavelength to Energy**:
- First, convert the wavelength from angstroms to meters:
\[ \lambda = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} \]
- Now substitute the values into the energy formula:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{4000 \times 10^{-10} \, \text{m}} \]
- Calculate \( E \):
\[ E = \frac{1.989 \times 10^{-25}}{4000 \times 10^{-10}} = 4.9725 \times 10^{-19} \, \text{J} \]
- Convert energy from Joules to electron volts (1 eV = \( 1.6 \times 10^{-19} \, \text{J} \)):
\[ E = \frac{4.9725 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 3.11 \, \text{eV} \]

4. **Compare Incident Energy with Work Functions**:
- Now we compare the calculated energy (3.11 eV) with the work functions of each element:
- A: 2 eV (3.11 > 2) → Emits electrons
- B: 2.4 eV (3.11 > 2.4) → Emits electrons
- C: 2.8 eV (3.11 > 2.8) → Emits electrons
- D: 3.2 eV (3.11 < 3.2) → Does not emit electrons

5. **Conclusion**:
- The elements that will emit photoelectrons are A, B, and C.

### Final Answer:
The elements which emit photoelectrons are A, B, and C.

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