According to Moseley's law, the frequency of a spectral line in the X-ray spectrum varies as the square of the atomic number of the element. Let's understand why this is the correct answer.

1. Moseley's Law:
Moseley's law states that the square root of the frequency of X-ray spectral lines is directly proportional to the atomic number (Z) of the element. Mathematically, it can be represented as √ν ∝ Z, where ν is the frequency of the spectral line.

2. Experimental Observations:
Moseley conducted experiments by bombarding different elements with high-energy electrons to produce X-rays. He observed that each element had a characteristic X-ray spectrum with distinct spectral lines. By measuring the frequencies of these spectral lines, he found a systematic relationship between the frequency and the atomic number.

3. X-ray Emission:
X-rays are emitted when high-energy electrons collide with the inner shell electrons of atoms, causing them to be ejected. The resulting vacancy is filled by an outer shell electron, which releases energy in the form of X-rays. Each element has a unique electron configuration, resulting in specific X-ray energies and frequencies.

4. Relationship with Atomic Number:
The atomic number of an element corresponds to the number of protons in its nucleus. As the atomic number increases, the number of protons also increases. This leads to a higher positive charge in the nucleus, resulting in stronger binding forces on the electrons.

5. Electron Energy Levels:
The energy levels of electrons in an atom are determined by the attractive forces between the electrons and the nucleus. Higher atomic numbers have more protons, leading to increased nuclear charge. This increased charge results in higher energy levels and tighter binding of electrons in the inner shells.

6. X-ray Frequency and Energy Levels:
The energy difference between the electron levels determines the frequency of the X-ray emitted. The frequency is directly proportional to the energy difference between the levels. As the atomic number increases, the energy difference between the electron levels also increases, leading to higher X-ray frequencies.

7. Square of Atomic Number:
Based on experimental observations, Moseley found that the square root of the X-ray frequency is directly proportional to the atomic number. This relationship implies that the X-ray frequency varies as the square of the atomic number.

In conclusion, Moseley's law states that the frequency of a spectral line in the X-ray spectrum varies as the square of the atomic number of the element. This relationship arises due to the correlation between the atomic number, electron energy levels, and X-ray frequencies.