The threshold wavelength for photo electric emission from a material is `5000A^(0)`. Photo electrons will be emitted when the material is illuminated with monochromatic radiation from

Options

A. 100 watt infrared lamp
B. 1 watt infrared lamp
C. 50 watt sodium vapour lamp
D. 50 watt ultra violet lamp

Answer

To solve the problem regarding the threshold wavelength for photoelectric emission, we need to determine the conditions under which photoelectrons will be emitted when the material is illuminated with monochromatic radiation.

### Given Data:
- Threshold wavelength (λ₀) = 5000 Å (Angstroms)

### Step-by-Step Solution:

**Step 1: Convert the threshold wavelength to meters.**
1 Å = 1 x 10^-10 m, therefore:
\[ \lambda_0 = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

**Step 2: Use the photoelectric effect equation.**
The photoelectric effect states that photoelectrons will be emitted if the energy of the incoming photons is greater than or equal to the work function (φ) of the material. The energy of a photon is given by:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) = Planck's constant = \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( c \) = Speed of light = \( 3 \times 10^8 \, \text{m/s} \)

**Step 3: Calculate the energy corresponding to the threshold wavelength.**
Using the threshold wavelength:
\[ E_0 = \frac{hc}{\lambda_0} \]
Substituting the values:
\[ E_0 = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{5 \times 10^{-7} \, \text{m}} \]
\[ E_0 = \frac{1.9878 \times 10^{-25}}{5 \times 10^{-7}} \]
\[ E_0 = 3.9756 \times 10^{-19} \, \text{J} \]

**Step 4: Determine the condition for photoelectron emission.**
Photoelectrons will be emitted when the energy of the incoming monochromatic radiation (E) is greater than or equal to the energy corresponding to the threshold wavelength (E₀):
\[ E \geq E_0 \]
This means that the wavelength (λ) of the incoming radiation must satisfy:
\[ \lambda \leq \lambda_0 \]

**Step 5: Convert the threshold energy back to wavelength.**
To find the maximum wavelength that can cause photoemission:
\[ \lambda = \frac{hc}{E} \]
For photoelectrons to be emitted, the wavelength must be less than or equal to 5000 Å.

### Conclusion:
Photoelectrons will be emitted when the material is illuminated with monochromatic radiation of wavelength less than or equal to 5000 Å.