Atoms, Nuclei & Radioactivity Test - 4

The plum pudding model is one of several scientific models of the atom. According to J.J. Thomson atomic models the positive particles in the atom form something like the "batter "in a plum pudding, while the negative electrons are scattered through this "batter ".

A spectrum is an assembly of energy levels in the form of radiations emitted by an atom in its excited state. Every atom gives discontinuous line spectra. Each line in the spectra corresponds to a specific wavelength and it is unique to a given element so no two elements give the same pattern of lines in their spectra.

Using formula for Paschen series,
1/λ=R[(1/3² )-1/n₂² ],n₂ =4,5,6 ….
For shortest wavelength, n₂ =∞
∴1/λ=R[(1/3² )-1/∞² ],n₂ =R/9 or λ=9/R ≈820.4 nm

The average angle of deflection of α-particles by a thin gold foil predicted by Thomson ’s model is about the same size as predicted by Rutherford ’s model. This is because the average angle was taken in both models.

Bohr model of the hydrogen atom attempts to plug in certain gaps as suggested by Rutherford ’s model by including ideas from the newly developing Quantum hypothesis. According to Rutherford ’s model, an atom has a central nucleus and electron/s revolve around it like the sun-planet system.
However, the fundamental difference between the two is that, while the planetary system is held in place by the gravitational force, the nucleus-electron system interacts by Coulomb ’s Law of Force. This is because the nucleus and electrons are charged particles. Also, an object moving in a circle undergoes constant acceleration due to the centripetal force.
Further, electromagnetic theory teaches us that an accelerating charged particle emits radiation in the form of electromagnetic waves. Therefore, the energy of such an electron should constantly decrease and the electron should collapse into the nucleus. This would make the atom unstable.
The classical electromagnetic theory also states that the frequency of the electromagnetic waves emitted by an accelerating electron is equal to the frequency of revolution. This would mean that, as the electron spirals inwards, it would emit electromagnetic waves of changing frequencies. In other words, it would emit a continuous spectrum. However, actual observation tells us that the electron emits a line spectrum.
 

Bohr never assumed stable electron orbits with the electronic angular momentum quantized as l=mvr=(nh/2 π)​Quantization of angular momentum means that the radius of the orbit and the energy will be quantized as well. Bohr assumed that the discrete lines seen in the spectrum of the hydrogen atom were due to transitions of an electron from one allowed orbit/energy to another.

A hydrogen atom has magnetic properties because the motion of the electron acts as a current loop. The energy levels of a hydrogen atom associated with orbital angular momentum are split by an external magnetic field because the orbital angular magnetic moment interacts with the field.

In Rutherford 's model we have a large massive core called the nucleus whereas, in Thomson 's model we do not have. Thus the probability of backward scattering by Thomson 's model is much less than that predicted by Rutherford model.