Q.Calculate the radius of dynamically stable orbit in hydrogen atom and total energy of their electron in the orbit by Rutherford nuclear model of the atom.

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.

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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.

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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 i …

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 wo …

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.

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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) …

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 ch …

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 contin …