Atoms, Nuclei & Radioactivity Test - 5

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/n₂ 2 ​​])
where, R = Rydberg constant =  1.097 ×10⁷ ×10⁻⁹ nm⁻¹ =1.097 ×10⁻² nm⁻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 ×10⁻² nm −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.
 h ν= 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 /2 π​. It is an integral multiple of h/2 π​.

The distance of closest approach is given as
r₀ = (1/4 πε₀ )(2Ze² /E)
Here,
Z= 75
e = 1.6x10^-19 C
E = 5 MeV = 5 X 1.6 X 10^-13 J
1/4 πε₀ = 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.