The metal that shows photoelectric emission at lowest frequency radiation is

Options

A. beryllium
B. lithium
C. sodium
D. magnesium

Answer

To solve the question regarding which metal shows photoelectric emission at the lowest frequency radiation, we can follow these steps:

### Step 1: Understand the Concept of Photoelectric Emission
Photoelectric emission refers to the phenomenon where electrons are emitted from a metal surface when it is exposed to light of sufficient frequency. The frequency of light must be above a certain threshold frequency for the emission to occur.

**Hint:** Remember that the threshold frequency is related to the energy required to remove an electron from the metal surface.

### Step 2: Define Threshold Frequency
The threshold frequency (ν₀) is the minimum frequency of incident light required to eject an electron from the surface of a metal. It is directly related to the work function (φ) of the metal, which is the minimum energy needed to remove an electron.

**Hint:** The relationship between energy and frequency is given by the equation E = hν, where h is Planck's constant.

### Step 3: Identify the Relationship Between Ionization Potential and Threshold Frequency
Metals with lower ionization potentials typically have lower threshold frequencies. This is because a lower ionization potential means that less energy is required to remove an electron from the metal.

**Hint:** Consider the periodic trends in ionization energy; elements with fewer valence electrons usually have lower ionization energies.

### Step 4: Analyze the Given Options
From the options provided, we need to identify which metal has the lowest ionization potential. Sodium (Na) is known to have a low ionization potential due to its single unpaired electron in the outermost shell, making it easier to remove.

**Hint:** Compare the ionization potentials of the metals listed; the one with the least value will be the answer.

### Step 5: Conclusion
Based on the analysis, sodium (Na) has the lowest ionization potential among the given options and therefore will show photoelectric emission at the lowest frequency radiation.

**Final Answer:** The metal that shows photoelectric emission at the lowest frequency radiation is Sodium (Na).