Which of the following metal requires radiation of the lowest wavelength to cause emission of electrons?

Options

A. `Na`
B. `K`
C. `Mg`
D. `Ca`

Explanation

To determine which metal requires radiation of the lowest wavelength to cause emission of electrons, we can follow these steps:

### Step 1: Understand the Concept of Ionization Energy
Ionization energy is the energy required to remove an electron from an atom. The higher the ionization energy, the more energy (or shorter wavelength radiation) is needed to remove an electron.

### Step 2: Identify the Metals and Their Groups
The metals given in the options are Sodium (Na), Potassium (K), Magnesium (Mg), and Calcium (Ca). Sodium and Potassium belong to Group 1 (alkali metals), while Magnesium and Calcium belong to Group 2 (alkaline earth metals).

### Step 3: Compare Ionization Energies
- **Group 1 (Alkali Metals)**: Sodium (Na) and Potassium (K) have lower ionization energies compared to Group 2 elements.
- **Group 2 (Alkaline Earth Metals)**: Magnesium (Mg) has a higher ionization energy than Calcium (Ca).

### Step 4: Order of Ionization Energies
The general trend for ionization energies is that they increase across a period and decrease down a group. Therefore, we can establish the following order:
- Mg > Ca (within Group 2)
- Na > K (within Group 1)

Combining these, we can deduce:
- Mg > Ca > Na > K

### Step 5: Determine Wavelength and Frequency Relationship
The energy of radiation is inversely proportional to its wavelength, given by the equation:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( E \) = energy
- \( h \) = Planck's constant
- \( c \) = speed of light
- \( \lambda \) = wavelength

Since higher ionization energy corresponds to higher energy radiation, it also corresponds to shorter wavelengths.

### Step 6: Conclusion
From the order of ionization energies, Magnesium (Mg) has the highest ionization energy among the given options, which means it requires radiation of the highest frequency (or lowest wavelength) to cause emission of electrons.

Thus, the correct answer is **Magnesium (Mg)**.

### Final Answer
The metal that requires radiation of the lowest wavelength to cause emission of electrons is **Magnesium (Mg)**.

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