The threshold wavelength for photoelectric emission for a material is `5200 A^(@)`. Will the photoelectrons be emitted when this material is illuminated with monochromatic radiation from 1 watt ultra violet lamp?

Explanation

To determine whether photoelectrons will be emitted when a material with a threshold wavelength of 5200 Å is illuminated with monochromatic radiation from a 1 watt ultraviolet lamp, we can follow these steps:

### Step 1: Understand the Threshold Wavelength
The threshold wavelength (λ₀) is the maximum wavelength of light that can cause photoelectric emission from a material. For this problem, λ₀ = 5200 Å (angstroms).

### Step 2: Convert the Threshold Wavelength to Meters
To work with standard units, convert the threshold wavelength from angstroms to meters:
\[ \lambda_0 = 5200 \, \text{Å} = 5200 \times 10^{-10} \, \text{m} = 5.2 \times 10^{-7} \, \text{m} \]

### Step 3: Calculate the Threshold Frequency
The threshold frequency (ν₀) can be calculated using the formula:
\[ \nu_0 = \frac{c}{\lambda_0} \]
where \( c \) is the speed of light (\( c \approx 3 \times 10^8 \, \text{m/s} \)).
Substituting the values:
\[ \nu_0 = \frac{3 \times 10^8 \, \text{m/s}}{5.2 \times 10^{-7} \, \text{m}} \approx 5.77 \times 10^{14} \, \text{Hz} \]

### Step 4: Determine the Wavelength of Ultraviolet Light
Ultraviolet (UV) light has a wavelength that is typically shorter than visible light. The wavelength of UV light is generally less than 5200 Å. For example, UV light can range from about 10 nm (1000 Å) to 400 nm (4000 Å). Therefore, we can assume:
\[ \lambda_{UV} < 5200 \, \text{Å} \]

### Step 5: Compare the Wavelengths
Since the wavelength of the ultraviolet light (λ_{UV}) is less than the threshold wavelength (λ₀), the condition for photoelectric emission is satisfied:
\[ \lambda_{UV} < \lambda_0 \]

### Step 6: Conclusion
Since the wavelength of the ultraviolet light is less than the threshold wavelength, photoelectrons will be emitted when the material is illuminated with the 1 watt ultraviolet lamp.

### Final Answer
Yes, photoelectrons will be emitted when the material is illuminated with monochromatic radiation from a 1 watt ultraviolet lamp.

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