Q.Choose the correct alternative from the clues given at the end of each statement:

(a) The key idea is that Thomson’s model had the atom as a uniform sphere of positive charge with electrons embedded inside, while Rutherford’s model had a tiny, dense nucleus. The size of the atom in both models is essentially the same — the overall atomic radius is determined by the electron cloud, which is comparable in both.

(b) In Thomson’s model, electrons are embedded in a uniform positive sphere and can be in stable equilibrium at certain positions. In Rutherford’s model, electrons orbit the nucleus and, according to classical electrodynamics, they must continuously radiate energy and spiral in — so they always experience a net force (centripetal) and are never in static equilibrium.

(c) Rutherford’s model is a classical planetary model. According to Maxwell’s equations, an accelerating charged particle (the orbiting electron) radiates energy, loses kinetic energy, and collapses into the nucleus. Thomson’s model has no such radiation problem because the electrons are stationary.

(d) Thomson’s model has a uniform positive sphere, so mass (due to positive charge) is nearly continuous throughout the atom. Rutherford’s model has almost all mass concentrated in the tiny nucleus, making the mass distribution highly non-uniform.

(e) In Thomson’s model, mass is distributed uniformly across the positive sphere, but the electrons contribute negligible mass. In Rutherford’s model, the nucleus contains nearly all the mass. So in both models, the positively charged part carries most of the mass.

The Concept and Intuition (Scale Analogy)

Imagine two ways to build an atom.

Thomson’s model (plum pudding) is like a spherical, positively charged jelly with tiny negative electrons embedded like raisins. The jelly is spread uniformly throughout the whole atom. So the positive charge and mass are continuous — every part of the atom has some positive charge and mass. An electron inside this jelly feels a restoring force toward the centre (like a ball in a bowl), so it can be in stable equilibrium at the centre.

Rutherford’s model (nuclear model) is like a tiny, heavy, positively charged marble (the nucleus) at the centre of a vast empty sphere, with electrons orbiting far away like planets around the Sun. The positive charge and almost all the mass are concentrated in that tiny nucleus. An electron orbiting this nucleus is constantly accelerating (changing direction), so according to classical physics it must radiate energy and spiral inward — the atom is doomed to collapse.

Now let’s match each statement.

Step-by-Step Reasoning

1. Statement (a): “The size of the atom in Thomson’s model is … the atomic size in Rutherford’s model.”

In Thomson’s model, the positive sphere defines the entire atom — its radius is the atomic radius. In Rutherford’s model, the atom’s size is determined by the electron orbits, which are about $10^{-10}$ m, while the nucleus is tiny ($\sim 10^{-15}$ m). The overall atomic size (the region where electrons exist) is the same order of magnitude in both models — roughly $10^{-10}$ m. So they are no different from each other in overall size.

2. Statement (b): “In the ground state of … electrons are in stable equilibrium, while in … electrons always experience a net force.”

• In Thomson’s model, an electron at the centre of the positive sphere feels zero net force (balanced from all sides). If displaced, it experiences a restoring force proportional to displacement — so it is in stable equilibrium.
• In Rutherford’s model, an electron in a circular orbit is always accelerating toward the nucleus (centripetal force). It never sits still; it always experiences a net force. There is no stable static equilibrium.

So the first blank is Thomson’s model, the second is Rutherford’s model.

3. Statement (c): “A classical atom based on … is doomed to collapse.”

Classical electrodynamics says an accelerating charge radiates energy. In Rutherford’s model, the orbiting electron is accelerating, so it loses energy and spirals into the nucleus — collapse. Thomson’s model has static electrons (no acceleration), so no radiation and no collapse. The answer is Rutherford’s model.

4. Statement (d): “An atom has a nearly continuous mass distribution in … but has a highly non-uniform mass distribution in …”

• Thomson’s model: positive charge (and mass) is spread uniformly throughout the sphere — continuous.
• Rutherford’s model: almost all mass is concentrated in the tiny nucleus — highly non-uniform.

So first blank: Thomson’s model; second blank: Rutherford’s model.

5. Statement (e): “The positively charged part of the atom possesses most of the mass in …”

• In Rutherford’s model, the nucleus is positively charged and contains nearly all the mass.
• In Thomson’s model, the positive sphere is spread out and contains most of the mass as well (electrons are very light). So both models have the positively charged part carrying most of the mass.

Thus the answer is both the models.

Method: Comparative Model Analysis

This method works by directly comparing the key structural features of Thomson's and Rutherford's atomic models — charge distribution, mass distribution, and electron stability — and then applying those features to each statement.

Step 1 — Recall the core features of each model

Thomson's model (plum pudding):

• Atom is a sphere of uniform positive charge.
• Electrons are embedded like raisins in a pudding.
• Positive charge and mass are spread continuously throughout the sphere.
• Electrons are in stable equilibrium (net force zero) when at rest inside the sphere.

Rutherford's model (nuclear):

• Atom has a tiny, dense, positively charged nucleus at the centre.
• Most of the atom is empty space.
• Electrons orbit the nucleus like planets around the Sun.
• Electrons always experience a net centripetal force (from the Coulomb attraction), so they are not in static equilibrium.
• According to classical electrodynamics, an accelerating electron radiates energy and spirals into the nucleus — hence the model is "doomed to collapse."

Step 2 — Apply the features to each statement

(a) The size of the atom in Thomson's model is the same as in Rutherford's model — both models place the atom's radius at roughly $10^{-10}$ m. The difference is in the internal structure, not the overall size.

Answer: no different from

(b) In Thomson's model, an electron placed anywhere inside the uniform positive sphere experiences a restoring force proportional to its displacement — at the centre, the net force is zero, so it can be in stable equilibrium. In Rutherford's model, an orbiting electron always has a centripetal acceleration and hence a net force toward the nucleus.

Answer: Thomson's model / Rutherford's model

(c) Rutherford's model has electrons accelerating continuously (circular motion is accelerated motion). Classical electromagnetism says an accelerating charge radiates energy, so the electron loses energy and spirals into the nucleus. Thomson's model has no such problem because the electrons are stationary (or move without acceleration in certain configurations).

Answer: Rutherford's model

(d) In Thomson's model, positive charge and mass are spread uniformly throughout the sphere — a nearly continuous distribution. In Rutherford's model, almost all the mass is concentrated in the tiny nucleus, so the mass distribution is highly non-uniform.

Answer: Thomson's model / Rutherford's model

(e) In Rutherford's model, the nucleus contains nearly all the atom's mass. In Thomson's model, the positive sphere also contains most of the mass (electrons are very light). So both models agree that the positively charged part carries most of the mass.

Answer: both the models

Final answers

1. no different from
2. Thomson's model / Rutherford's model
3. Rutherford's model
4. Thomson's model / Rutherford's model
5. both the models

Here are the common mistakes students make on this Scale Analogy exercise, along with the reasoning to avoid each.

Mistake 1: Confusing "size" with "nuclear density" in part (a)

Students often think Rutherford's atom is "larger" because they remember the nucleus is tiny and dense. They pick much greater than for Thomson's model.

Why this is wrong: The question asks about the size of the atom, not the size of the nucleus. In Thomson's model, the positive charge and mass are spread throughout the entire sphere. In Rutherford's model, the atom is mostly empty space, but the outer boundary (the electron orbits) is actually much larger than Thomson's sphere. Rutherford's scattering experiment showed that the atom is mostly empty, meaning the electrons are far from the nucleus, making the atomic radius about 10,000–100,000 times larger than the nuclear radius.

How to avoid: Always distinguish between "size of the atom" (the whole thing) and "size of the nucleus" (the tiny core). For atomic size, Rutherford's model is vastly larger.

Mistake 2: Misapplying "stable equilibrium" in part (b)

Students think that because Rutherford's model has a central nucleus, the electrons are "held" by electrostatic attraction, so they must be in stable equilibrium. They pick Rutherford's model for the first blank.

Why this is wrong: In Rutherford's model, an electron orbiting a nucleus is accelerating (centripetal acceleration). According to classical electrodynamics, an accelerating charge radiates energy. The electron loses energy, spirals inward, and experiences a net force (the centripetal force). It is not in stable equilibrium — it is in a dynamic, unstable state. In Thomson's model, the electrons are embedded in a uniform positive sphere. At certain positions inside the sphere, the net electrostatic force on an electron can be zero (equilibrium), and if displaced slightly, it experiences a restoring force (like a spring), making it stable equilibrium.

How to avoid: Remember: "Stable equilibrium" means if you push it slightly, it comes back. Thomson's model gives that (electrons oscillate about their equilibrium positions). Rutherford's model gives a net force always (the centripetal force), and the electron is doomed to collapse.

Mistake 3: Forgetting which model "collapses" in part (c)

Students sometimes pick Thomson's model because they think "plum pudding" sounds unstable.

Why this is wrong: Thomson's model is actually classically stable — the electrons can sit at rest inside the positive sphere. Rutherford's model is the one that is "doomed to collapse" because the orbiting electron must radiate energy and spiral into the nucleus. This is the famous "classical atom" problem that led to Bohr's model.

How to avoid: Link the word "collapse" to the radiation problem. Only Rutherford's model has accelerating charges (orbiting electrons). Thomson's model has stationary electrons — no acceleration, no radiation, no collapse.

Mistake 4: Mixing up "continuous" vs "non-uniform" mass distribution in part (d)

Students think Rutherford's model has a "continuous" mass distribution because the electrons are spread out.

Why this is wrong: "Continuous mass distribution" means the mass is spread smoothly throughout the volume, with no empty gaps. That describes Thomson's model (positive charge and mass are uniformly distributed). Rutherford's model has a highly non-uniform mass distribution: almost all the mass is concentrated in a tiny nucleus, and the rest is empty space.

How to avoid: Visualize the two models. Thomson: a blob of positive pudding with raisins. Rutherford: a tiny, dense marble (nucleus) in a vast empty stadium with a few specks (electrons) whizzing around. The first is continuous; the second is extremely non-uniform.

Mistake 5: Forgetting that Thomson's model also has positive charge in part (e)

Students think only Rutherford's model has a positively charged part that possesses most of the mass. They pick Rutherford's model only.

Why this is wrong: In Thomson's model, the positive charge is spread throughout the sphere, and it also contains most of the mass (since electrons are very light). So the statement "the positively charged part of the atom possesses most of the mass" is true for both models. The difference is where that positive charge is located (spread out vs. concentrated).

How to avoid: Read carefully: "possesses most of the mass" — in both models, the positive part carries nearly all the mass. The question is not about distribution, just about which part holds the mass.