Atoms And Nuclei

Step 1: Structure of an atom.
An atom consists of a very small central nucleus surrounded by electrons that move in large orbits around it. The nucleus contains protons and neutrons which together account for almost the entire mass of the atom.

Step 2: Size comparison between atom and nucleus.
The size of a nucleus is extremely small compared to the size of the atom. The radius of an atom is about whereas the radius of a nucleus is about . Thus the nucleus occupies only a tiny fraction of the total volume of the atom.

Step 3: Distribution of mass in an atom.
Almost the entire mass of an atom is concentrated within the nucleus, while the surrounding region where electrons move contains very little mass but occupies most of the volume of the atom.

Step 4: Effect on density.
Since density is defined as mass divided by volume, the nucleus has a very large density because nearly the whole mass of the atom is packed into an extremely small volume.

Step 5: Conclusion.
Therefore, the density of a nucleus is much greater than that of the atom because the atomic mass is concentrated in a very small nuclear volume while the atom itself occupies a much larger space.

Step 1: Radius of a nucleus.
The radius of a nucleus is given by the empirical relation:
where is a constant ( ) and is the mass number of the nucleus.

Step 2: Volume of the nucleus.
The volume of a nucleus is given by the formula for the volume of a sphere:
Substituting :


Step 3: Mass of the nucleus.
The mass of the nucleus is approximately proportional to the mass number:
where is the mass of a nucleon (proton or neutron).

Step 4: Density of nuclear matter.
Density is defined as:
Substituting the values:


Step 5: Conclusion.
Since the mass number cancels out, the density does not depend on the size of the nucleus. Therefore, the density of nuclear matter is approximately the same for all nuclei.

Step 1: Understanding the Balmer series.
The Balmer series corresponds to electronic transitions in the hydrogen atom where an electron falls from a higher energy level to the second energy level . These transitions produce spectral lines in the visible region of the electromagnetic spectrum.
Step 2: First line of the Balmer series.
The first spectral line of the Balmer series occurs when an electron transitions from the third energy level to the second energy level, that is This line is known as the H line.
Step 3: Second line of the Balmer series.
The second spectral line occurs when the electron falls from the fourth energy level to the second energy level: This line is known as the H line in the hydrogen spectrum.
Step 4: Analysis of options.

• (A) : Incorrect. This corresponds to the first spectral line of the Balmer series.
• (B) : Incorrect. This transition belongs to the Paschen series, not the Balmer series.
• (C) : Correct. This produces the second spectral line of the Balmer series.
• (D) : Incorrect. This represents the series limit of the Balmer series.

Step 5: Conclusion.
Therefore, the second spectral line of the Balmer series corresponds to the transition of an electron from the fourth energy level to the second energy level.
Final Answer: and .