Which of the following metal requires radiation of highest frequency to cause emission of electrons?

Options

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

Answer

To determine which metal requires radiation of the highest frequency to cause the emission of electrons, we need to analyze the ionization energies of the given metals: magnesium (Mg), calcium (Ca), potassium (K), and sodium (Na).

### Step-by-Step Solution:

1. **Understanding Ionization Energy**:
- Ionization energy is the energy required to remove an electron from an atom in the gaseous state. Higher ionization energy means that more energy (or higher frequency radiation) is needed to remove an electron.

2. **Relationship Between Energy and Frequency**:
- The relationship between energy (E) and frequency (ν) is given by the equation:
\[ E = hν \]
where \( h \) is Planck's constant. This means that higher energy corresponds to higher frequency radiation.

3. **Trends in Ionization Energy**:
- Ionization energy increases across a period (from left to right in the periodic table) and decreases down a group (from top to bottom).
- For the metals given:
- Sodium (Na) and potassium (K) are in Group 1, with potassium being lower in the group, thus having lower ionization energy.
- Magnesium (Mg) and calcium (Ca) are in Group 2, with magnesium being higher in the group than calcium.

4. **Comparing Ionization Energies**:
- Among the given metals:
- Sodium (Na) has the lowest ionization energy.
- Potassium (K) has even lower ionization energy than sodium.
- Calcium (Ca) has a lower ionization energy than magnesium (Mg).
- Magnesium (Mg) has the highest ionization energy among the four metals.

5. **Conclusion**:
- Since magnesium has the highest ionization energy, it will require radiation of the highest frequency to cause the emission of electrons.

### Final Answer:
- The metal that requires radiation of the highest frequency to cause the emission of electrons is **Magnesium (Mg)**.