Class 12 : Chapter 12 : Atoms

  

Atoms 

Atoms

  All elements consists of very small invisible particles, called atom. Every atom is a sphere of radius of the order of 10-10 m, in which entire mass is uniformly distributed and negative charged electrons revolve around the nucleus.

Thomson’s Model of an Atom: 

An atom consists of positively charged matter in which the negatively charged electrons are uniformly embedded like plums in a pudding. This model could not explain scattering of alpha-particles through thin foils and hence discarded.

Rutherford’s Model of an Atom: 

Basic assumption of Rutherford’s atomic model:
(i) Atom consists of small central core, called atomic nucleus in which whole mass and positive charge is assumed to be concentrated.
(ii) The size of nucleus is much smaller than the size of the atom.
(iii) The nucleus is surrounded by electrons and atom is electrically neutral.

(iv) Electrons revolves around the nucleus and centripetal force is of electrostatic nature. 

Geiger and Marsden in their experiment on scattering of alpha-particles found that most of the alpha-particles passed undeviated through thin foils but some of them were scattered through very large angles.

From the results of these experiments, Rutherford proposed the following model of an atom:-

a)  An atom consists of a small and massive central core in which the entire positive charge and almost the whole mass of the atom are concentrated. This core is called the nucleus.

b)  The nucleus occupies a very small space as compared to the size of the atom.

c)  The atom is surrounded by a suitable number of electros so that their total negative charge is equal to the total positive charge on the nucleus and the atom as a whole is electrically neutral.

d) The electrons revolve around the nucleus in various orbits just as planets revolve around the sun.

e)  The centripetal force required for their revolution is provided by the electrostatic attraction between the electrons and the nucleus.

2. Experimental arrangement for α-scattering experiment and trajectory followed by α -particles

Draw-back of Rutherford Model: 

This model could not explain instability of the atom because according to classical electromagnetic theory the electron revolving around the nucleus must continuously radiate energy in the form of electromagnetic radiation and hence it should fall into the nucleus.

  Drawbacks of Rutherford’s Model were
(i) It could not explained stability of atom clearly.
(ii) It was unable to explain line spectrum of Hydrogen atom.

Distance of Closest Approach: 

When an alpha-particle of mass m and velocity v moves directly towards a nucleus of atomic number Z, its initial energy E, which is just the kinetic energy K gets completely converted into potential energy U at stopping point. This stopping point happens to be at a distance of closest approach d from the nucleus.

Hence,

Impact Parameter:

a)  It is defined as the perpendicular distance of the velocity of the alpha-particle from the centre of the nucleus, when it is far away from the atom.

b) The shape of the trajectory of the scattered alpha-particle depends on the impact parameter b and the nature of the potential field.

c)  Rutherford deduced the following relationship between the impact parameter b and the scattering angle :-

Quantisation or Discretisation: 

The quantization or discretisation of a physical quantity means that it cannot have any arbitrary value but can change only to take certain specific value.

Bohr’s Model for the Hydrogen Atom: 

Basic postulates:-

a)  Nuclear concept: 

An atom consists of a small massive centre called nucleus around which planetary electrons revolve. The centripetal force required for their rotation is provided by the electrostatic attraction between the electrons and the nucleus.

b)  Quantum condition: 

Of all the possible circular orbits allowed by the classical theory, the electrons are permitted to circulate only in such orbits in which the angular momentum of an electron is an integral multiple of , h being Planck’s constant.

 

where n is called principal quantum number.

c)  Stationary orbits: 

While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.

d)  Frequency condition: 

An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit. If E1 and E2 are the energies associated with these permitted orbits then the frequency  of the emitted/absorbed radiation is,

e)  Radius of the orbit of an electron in hydrogen atom is, 

f)  Kinetic energy K & electrostatic potential energy U of the electron in hydrogen atom:-

g)  Total energy E of the electron in hydrogen atom:-

h)  Speed of an electron in the nth orbit is,

 

Where  

is fine structure constant.

i)  Energy of an electron in nth orbit is,

Failure of Bohr’s Model:

a)  This model is applicable only to hydrogen-like atoms and fails in case of higher atoms.

b)  It could not explain the fine structure of the spectral lines in the spectrum of hydrogen atom.

Energy Level Diagram:

 It is a diagram in which the energies of the different stationary states of an atom are represented by parallel horizontal lines, drawn according to some suitable energy scale.

Spectral Series of Hydrogen Atom: 

Whenever an electron in hydrogen atom makes a transition from a higher energy level n2 to a lower energy level n1, the difference of energy appears in the form of a photon of frequency  is given by-

Different Spectral Series of Hydrogen Atom:

These are as follows:

Hydrogen spectrum contains five series, namely:

(i) Lyman Series 

When electron jumps from an orbit with  n = 2, 3,4, …orbit to the first orbit with  n = 1 orbit, then a line of Lyman series is obtained.

This series lies in ultra violet region.

(ii) Balmer Series 

When electron jumps from  an orbit with  n = 3, 4, 5,… orbit  to the first orbit with n = 2 orbit, then a line of Balmer series is obtained.

This series lies in visual region.

(iii) Paschen Series 

When electron jumps from  an orbit with  n = 4, 5, 6,… orbit to the first orbit with  n = 3 orbit, then a line of Paschen series is obtained.

This series lies in infrared region

(iv) Brackett Series 

When electron jumps from  an orbit with n = 5,6, 7…. orbit to the first orbit with  n = 4 orbit, then a line of Brackett series is obtained.

This series lies in infrared region.

(v) Pfund Series 

When electron jumps from  an orbit with  n = 6,7,8, … orbit to the first orbit with  n = 5 orbit, then a line of Pfund series is obtained.

This series lies in infrared region.

Wave Model

It is based on wave mechanics. Quantum numbers are the numbers required to completely specify the state of the electrons.

In the presence of strong magnetic field, the four quantum numbers are

(i) Principal  quantum number (n) can have value 1,2, … ∞

(ii) Orbital angular momentum quantum or Azimuthal quantum number ( ℓ ) can have value 0,1, 2, … ,(n – 1).

(iii) Magnetic quantum number (m_e) which can have values – I to I.

(iv) Magnetic spin angular momentum quantum number ( m _s ) which can have only two value + 1 / 2.

Electron Orbitals  and their Shape:

Electron orbitals are the three-dimensional areas around the nucleus of an atom where a particular electron resides. Each orbital can hold two electrons. They are also known as atomic orbitals. Atomic orbitals come in different shapes, depending on the number of electrons the atom has.

Excitation Energy: 

It is defined as the energy required by an electron of an atom to jump from its ground state to any one of its existed state.

Ionisation Energy: 

 It is defined as the energy required to remove an electron from an atom, i.e., the energy required to take an electron from its ground state to the outermost orbit (n = )

Excitation Potential: 

It is the accelerating potential which gives sufficient energy to a bombarding electron, so to excite the target atom by raising one of its electrons from an inner to and outer orbit.

Ionisation Potential: 

It is the accelerating potential which gives to bombarding electron, sufficient energy to ionize the target atom by knocking one of its electrons completely out of the atom.

De Broglie’s Hypothesis: 

Louis de Broglie was a student of Bohr, who then formulated his own hypothesis of wave-particle duality, drawn from this understanding of light. Later on, when this hypothesis was proven true, it became a very important concept in particle physics. 
The concept that matter behaves like wave is called the de Broglie hypothesis, named after Louis de Broglie, who proposed it in 1924.
The electrons having a wavelength

gave an explanation for Bohr’s quantised orbits by bringing in the wave-particle duality. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.

From de Broglie equation for a material particle, i.e., 

  we conclude the following:

i. If v = 0, then λ = ∞, and

If v = ∞, then λ = 0

It means that waves are associated with the moving material particles only. This implies these waves are independent of their charge. 

de Broglie gave the following equation which can be used to calculate de Broglie wavelength, $\lambda$, of any massed particle whose momentum is known:

$$\lambda = \frac{h}{p},

where $h$ is the Plank's constant and $p$ is the momentum of the particle whose wavelength we need to find.

With some modifications the following equation can also be written for velocity $(v)$ or kinetic energy $(K)$ of the particle (of mass $m$):

$$\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mK}}.

MASER:-

a)  Maser stands for ‘Microwave Amplification by Stimulated Emission of Radiation’.

b)  It is simply a device for producing a highly intense, monochromatic coherent and collimated beam of microwaves.

LASER:-

a)  It stand for ‘Light Amplification by Stimulated Emission of Radiation.

b)  It is a device used to produce highly intense strong monochromatic coherent and collimated beam of light.