The threshold wavelength for a photosensitive metal plate is 5000 Å. Photoelectrons will be emitted from it if it is irradiated by light from a

Options

A. 50 watt infrared lamp
B. red lamp emitting light wavelength of 7000 Å
C. 25 watt ultraviolet lamp
D. 25 watt infrared lamp

Explanation

To determine whether photoelectrons will be emitted from a photosensitive metal plate with a threshold wavelength of 5000 Å, we need to analyze the energy of the incident light and compare it with the threshold energy required to release the photoelectrons.

### Step-by-Step Solution:

1. **Understand the Threshold Wavelength**:
The threshold wavelength (λ_th) is given as 5000 Å (angstroms). This is the maximum wavelength of light that can still cause photoemission.

2. **Calculate the Energy Corresponding to the Threshold Wavelength**:
The energy (E) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( c \) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength in meters.

Converting 5000 Å to meters:
\[ 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5.0 \times 10^{-7} \, \text{m} \]

Now substituting the values into the energy formula:
\[ E_{th} = \frac{(6.626 \times 10^{-34} \, \text{Js})(3.00 \times 10^8 \, \text{m/s})}{5.0 \times 10^{-7} \, \text{m}} \approx 3.98 \times 10^{-19} \, \text{J} \]

3. **Determine the Wavelengths of the Given Light Sources**:
We need to check the wavelengths of the options provided to see if they are less than or equal to 5000 Å:
- Option 1: 4000 Å
- Option 2: 7000 Å
- Option 3: 3000 Å
- Option 4: 6000 Å

4. **Compare Each Wavelength with the Threshold Wavelength**:
- **Option 1 (4000 Å)**: This is less than 5000 Å. **Photoelectrons will be emitted.**
- **Option 2 (7000 Å)**: This is greater than 5000 Å. **Photoelectrons will not be emitted.**
- **Option 3 (3000 Å)**: This is less than 5000 Å. **Photoelectrons will be emitted.**
- **Option 4 (6000 Å)**: This is greater than 5000 Å. **Photoelectrons will not be emitted.**

5. **Conclusion**:
The light sources that will cause photoelectrons to be emitted from the metal plate are those with wavelengths of 4000 Å and 3000 Å.

### Final Answer:
Photoelectrons will be emitted from the photosensitive metal plate if it is irradiated by light from sources with wavelengths of 4000 Å and 3000 Å.