Test: Atoms - JEE MCQ

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/2π)​ 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.

In the Geiger-Marsden experiment very small deflection of the beam was expected because positive charge and the negative electrons are distributed through the whole atom reducing electric field inside the atom.

Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation. The most striking example of fluorescence occurs when the absorbed radiation is in the ultraviolet region of the spectrum, and thus invisible to the human eye, while the emitted light is in the visible region, which gives the fluorescent substance a distinct color that can be seen only when exposed to UV light. Fluorescent materials cease to glow nearly immediately when the radiation source stops, unlike phosphorescent materials, which continue to emit light for some time after.

In the alpha-particle scattering experiment, if a thin sheet of solid hydrogen is used in place of a gold foil, then the scattering angle would not be large enough. This is because the mass of hydrogen (1.67×10−27) is less than the mass of incident α−particles (6.64×10−27). Thus, the mass of the scattering particle is more than the target nucleus (hydrogen). As a result, the α−particles would not bounce back if solid hydrogen is used in the α−particle scattering experiment.

Energy at ground state E_1​=−13.6 eV
Energy at n=3: E_3​=−13.6/9​=1.5 eV
To excite it to n=3 energy given to electron is E₃​−E₁​=12.1 eV

In classical electromagnetic theory, atoms and molecules are considered to contain electrical charges (i.e. electrons, ions) which are regarded as oscillating about positions of equilibrium, each with its appropriate natural frequency, v0 . When placed in a radiation field of frequency v , each oscillator in the atom or molecule is set into forced vibration with the same frequency as that of the radiation. The amplitude of the forced vibration is small, but as v approaches v0 , the amplitude of the forced vibration increases rapidly. To account for the absorption of energy from the radiation field, it is necessary to assume that the oscillator in the atom or molecule must overcome some frictional force proportional to its velocity during its forced motion. For small amplitudes of forced oscillation, the frictional force, and therefore the absorption of energy, is negligible. Near resonance , the amplitude of oscillation becomes large, with a correspondingly large absorption of energy to overcome the frictional force. Therefore, the radiation of frequencies near the natural frequency of the oscillator corresponds to an absorption band.

Lines in the spectrum were due to transitions in which an electron moved from a higher-energy orbit with a larger radius to a lower-energy orbit with smaller radius. The orbit closest to the nucleus represented the ground state of the atom and was most stable; orbits farther away were higher-energy excited states.

In Thomson's model, the atom is composed of electrons surrounded by a soup of positive charge to balance the electrons' negative charges, like negatively charged “plums” surrounded by positively charged “pudding”. The 1904 Thomson model was disproved by Hans Geiger and Ernest Marsden's 1909 gold foil experiment.

1/ λ =Z². (both have same transition so same value of n)
λ /122=1/16
λ =122/16
=7.62nm

In the Geiger-Marsden experiment, at the point of closest approach the kinetic energy is zero and the electrical potential equals the initial kinetic energy supplied.

The phosphor fluoresces to produce light. A fluorescent bulb produces less heat, so it is much more efficient. This makes fluorescent bulbs four to six times more efficient than incandescent bulbs. That's why you can buy a 15-watt fluorescent bulb that produces the same amount of light as a 60-watt incandescent bulb.

An atom has a nearly continuous mass distribution in Thomson’s model, but has a highly non-uniform mass distribution in Rutherford’s model.

For single electron species,
1/λ​=RZ²[(1/n₁²​​)−(1/n₂2​​])
where, R = Rydberg constant =  1.097×10⁷×10⁻⁹nm⁻¹=1.097×10⁻²nm⁻¹
For Hydrogen atom, Z = Atomic number = 1
For Balmer series, n_1​ = 2 and for longest wavelength in Balmer series, minimum energy transition is to be considered because wavelength is inversely proportional to Energy.
So, n₂​ = 3
∴1/λ​=1.097×10⁻²nm−1×12[(1/2²)​−(1/3²)]
⇒λ=656nm

In 1913 Bohr proposed his quantized shell model of the atom to explain how electrons can have stable orbits around the nucleus. The motion of the electrons in the Rutherford model was unstable because, according to classical mechanics and electromagnetic theory, any charged particle moving on a curved path emits electromagnetic radiation; thus, the electrons would lose energy and spiral into the nucleus. To remedy the stability problem, Bohr modified the Rutherford model by requiring that the electrons move in orbits of fixed size and energy. The energy of an electron depends on the size of the orbit and is lower for smaller orbits. Radiation can occur only when the electron jumps from one orbit to another. The atom will be completely stable in the state with the smallest orbit, since there is no orbit of lower energy into which the electron can jump.
 hν = E_f−E_i

When Rutherford saw the results of the experiment by Geiger and Marsden, he said:
“It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
Rutherford used the results of this experiment to develop a new model for the atom. This model proposed a central nucleus with a positive charge. It was this positively charged nucleus that was responsible for the strong backward deflection of the positively charged alpha particles.
The model also proposed that negatively charged electrons surrounded this nucleus. However, as most of the alpha particles passed through the gold foil with no deflection at all, Rutherford realised that most of the atom was empty space. So, his model placed the electrons at some distance from the nucleus.
 

The angular momentum (L) of an electron in a Bohr orbit is given as L= nh /2π ​. It is an integral multiple of h/2π​.

The distance of closest approach is given as
r₀= (1/4πε₀)(2Ze²/E)
Here,
Z= 75
e = 1.6x10^-19 C
E = 5 MeV = 5 X 1.6 X 10^-13 J
1/4πε₀ = 9x10⁹ Nm2C-1
 so,
r₀ = [9x10⁹ x 2x75x(1.6x10^-19)2] / [5 X 1.6 X 10^-13] m
r₀=30x10⁻¹⁵ m
r₀=30

If light from a continuous spectrum passes through a cool, transparent gas we observe dark lines appear in the spectrum. The lines occur where atoms of the gas have absorbed specific wavelengths of light. Hence we call this type of spectrum an absorption spectrum.