The photoelectric threshold of a certain metal is `3000A`. If the radiation of `2000A` is incident on the metal

Options

A. electrons will be emitted
B. positrons will be emitted
C. protons will be emitted
D. electrons will no be emitted

Explanation

To determine whether electrons will be emitted from a metal when radiation of a certain wavelength is incident on it, we can follow these steps:

### Step 1: Understand the Photoelectric Effect
The photoelectric effect occurs when light of sufficient energy (or frequency) strikes a metal surface and causes the emission of electrons. The energy of the incident light must be greater than the work function (threshold energy) of the metal for electrons to be emitted.

### Step 2: Identify the Given Values
- **Threshold Wavelength (λ₀)**: 3000 Å (angstroms)
- **Incident Wavelength (λ)**: 2000 Å (angstroms)

### Step 3: Relate Wavelength to Energy
The energy of a photon can be expressed in terms of its wavelength using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( c \) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength of the light.

### Step 4: Calculate the Threshold Energy
The threshold energy (work function) corresponding to the threshold wavelength (λ₀) is given by:
\[ W = \frac{hc}{\lambda_0} \]
Substituting the threshold wavelength:
\[ W = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{3000 \times 10^{-10} \, \text{m}} \]

### Step 5: Calculate the Energy of the Incident Photon
Now calculate the energy of the incident photon using the incident wavelength (λ):
\[ E_{\text{incident}} = \frac{hc}{\lambda} \]
Substituting the incident wavelength:
\[ E_{\text{incident}} = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{2000 \times 10^{-10} \, \text{m}} \]

### Step 6: Compare Energies
To determine if electrons will be emitted, we need to check if the energy of the incident photon is greater than the work function:
\[ E_{\text{incident}} > W \]

### Step 7: Conclusion
If the energy of the incident photon is greater than the work function, electrons will be emitted. Since the threshold wavelength (3000 Å) is greater than the incident wavelength (2000 Å), this implies that the energy of the incident photon is greater than the work function. Therefore, electrons will be emitted.

### Final Answer
**Electrons will be emitted.**

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