Q.State the difficulties faced by Rutherford's atomic model.

Classical EM theory says an accelerating charge radiates energy; an electron in a circular orbit is accelerating, so it should continuously lose energy and spiral into the nucleus — this instability is Rutherford's model's fatal flaw.

In Rutherford's model, electrons revolve around the nucleus in circular orbits under the Coulomb force of attraction, which provides the centripetal acceleration needed for circular motion. But according to classical electrodynamics, any accelerated charged particle must radiate electromagnetic energy continuously.

As the orbiting electron radiates energy, its total energy (and hence orbital radius) would continuously decrease, causing it to spiral inward and eventually collapse into the nucleus in a fraction of a second — contrary to the observed stability of atoms. This is why Rutherford's purely classical planetary model could not explain atomic stability, motivating Bohr's quantized-orbit postulate.

An atom has Z protons (each +e) balanced by Z orbital electrons (each −e), so the net charge cancels exactly.

An atom of atomic number Z has a nucleus with Z protons, each carrying charge +e, giving total positive nuclear charge +Ze. Surrounding the nucleus are Z electrons, each carrying charge −e, giving total negative charge −Ze.

Net charge on the atom = (+Ze) + (−Ze) = 0

An atom is, by definition, electrically neutral as a whole (ions are what carry net charge, not neutral atoms).

An atom contains a positively charged nucleus (protons) surrounded by an equal number of negatively charged electrons, making the atom overall electrically neutral.

An atom consists of a small, dense, positively charged nucleus (made of protons and neutrons) surrounded by negatively charged electrons occupying the much larger surrounding space. In a neutral atom, the number of electrons exactly equals the number of protons, so the net charge of the atom is zero. Only when an atom loses or gains electrons does it become a charged ion (positive if it loses electrons, negative if it gains them) — the neutral atom itself is not a 'positive particle'.

Without circular motion, nothing counteracts the electron's electrostatic attraction toward the nucleus — it would simply be pulled straight in, collapsing the atom.

Reasoning

An electron orbits the nucleus because the Coulomb attraction between electron and nucleus supplies exactly the centripetal force needed for circular motion: $\dfrac{ke^2}{r^2} = \dfrac{mv^2}{r}$. If the electron were stationary (no orbital velocity), there would be no centripetal requirement to balance against — the unbalanced attractive Coulomb force would simply accelerate the electron straight toward the nucleus, and the electron would collapse into (or crash into) the nucleus almost instantly. Atoms as stable, extended structures would not exist.

Rutherford's nuclear model successfully explained the concentration of mass and charge but failed to account for atomic stability because accelerating electrons should radiate energy and spiral into the nucleus. The answer is (D).

Thomson's and Rutherford's models both give the atom an overall radius of about $10^{-10}$ m; what differs is where the positive charge sits, not the size of the atom itself.

In Thomson's model, the atom is a sphere of positive charge (radius $\sim 10^{-10}$ m) with electrons embedded in it like plums in a pudding — the positive charge is spread over the whole atomic volume.

In Rutherford's model, Rutherford's alpha-scattering experiment showed that the positive charge and almost all the mass are concentrated in a tiny central nucleus (radius $\sim 10^{-15}$ to $10^{-14}$ m), while the electrons orbit at distances that still make the overall atom about $10^{-10}$ m in radius.

So the nucleus is far smaller than Thomson had assumed, but the outer size of the atom itself (set by the electron orbits) is essentially the same order of magnitude in both models.

An atom is electrically neutral because the positive charge of its protons exactly balances the negative charge of its electrons.

An atom consists of a small, dense, positively charged nucleus (containing protons and neutrons) surrounded by negatively charged electrons revolving around it. The number of electrons orbiting the nucleus equals the number of protons in the nucleus (the atomic number Z). Since the magnitude of charge on a proton (+e) equals the magnitude of charge on an electron (−e), the total positive charge cancels the total negative charge, making the atom as a whole electrically uncharged (neutral). It only becomes charged (an ion) if it gains or loses electrons.

Ernest Rutherford discovered the atomic nucleus via his gold-foil (alpha-scattering) experiment.

In 1911, Rutherford's team fired alpha particles at a thin gold foil. Most passed straight through, but a small fraction scattered at large angles — some even bounced back. This could only be explained if almost all the atom's mass and its entire positive charge were concentrated in a tiny central region: the nucleus. This led Rutherford to propose the nuclear model of the atom.

Rutherford's model predicts atoms should collapse in an instant — it doesn't.

In Rutherford's nuclear model, electrons revolve around a small, dense, positively-charged nucleus under electrostatic attraction, in a manner analogous to planets orbiting the Sun. However, an electron moving in a circular orbit is constantly accelerating (centripetal acceleration towards the centre). According to classical electromagnetic theory, an accelerating charge must continuously radiate electromagnetic energy. As the electron loses energy, its orbital radius should continuously shrink, spiralling into the nucleus within a fraction of a second — predicting the atom is unstable and should collapse almost instantly. This directly contradicts the observed long-term stability of atoms. (Related drawback: this classical picture also predicts a continuous emission spectrum, not the sharp, discrete line spectra actually observed for atoms like hydrogen — Rutherford's model could not explain these either.)