What is nuclear force?

It is a force which is responsible for holding the nucleons ( proton and neutron ) in a nucleus and thus making the nucleus stable.

It has four types:
(1). n-n force
(2). p-p force
(3). p-n force
(4). n-p force

Main characteristics of Nuclear Force:-
(1). Nuclear forces are attractive forces and strongest among all the other forces.
(2). Nuclear forces are short range forces.
(3). Nuclear forces are operative within the range of  10¯¹³ cm. 
(4). Nuclear forces are central forces.
(5). Nuclear forces don't obey inverse square law

(6). Nuclear forces are charge independent.
(7). Nuclear forces are spin dependent. e.g.
      A complete of a proton and a neutron with parallel spin form a stable particle (deutron).
(8). Nuclear forces turn into strong repulsive forces when the distance between
       the nucleons becomes smaller as compared with nucleus diameter.

Assumptions:-
(1). The nuclear force ( n-n , p-p , n-p ) are assumed to be almost equal in magnitude and
       independent of charge of nucleons & supported by ( p-p , n-p ) scattering at lower energies.
      This assumption is known as "Hypothesis of charge independence of nuclear forces".
(2). The nuclear forces ( n-n , p-p ) are assumed to be nearly equal and must be smaller
       than ( n-p ) forces & supported by ( p-p , n-p ) scattering at high energies.
       This assumption is known as "Hypothesis of charge symmetry of nuclear forces".

What Is Group Velocity?

Group Velocity:
The ratio between frequency and wave no. is known as Group velocity..

Mathematically:

Group velocity= Vg = w/k
Where "w" is frequency of the wave & "k" is the wave number.

A group consists of a number of wave of different frequency superimposed upon each other. 
For example:
White colour consists of of a continuous visible wavelength spectra ranging about 300 nm to 700 nm. The motion of a such a pulse is described by its group velocity.
The wave velocity of each component of a such group is different in all medium except volume. 
Hence, such a group of wave will disperse with time, when it travels through a medium.
The important of a group velocity lies in the fact is the velocity which energy in the wave group is transmitted. e.g. For monochromatic wave, the group velocity and wave velocity are identical.

What Are Quarks?

What Are Quarks?
A quark is an elementary particle & is fundamental constituent particle of matter. Before the discovery of quark, atom is a fundamental particle of matter. Quark is the fermionic. i.e. Obeys Pauli exclusion Principle..
According to quark theory initiated by M-Gell-Mann & G-Zweig in 1994, the quarks are proposed as the basic building blocks of mesons and baryons. A pair of quark and anti-quark makes a meson (exchange particle between nucleons, that holds the nucleus together). The mass of mesons is equal to 200 times the mass of electron. Three quarks make a baryon.

Types Of Quarks?
There are six types of quarks, known as follows

• Up quark
• Down quark
• Strange quark
• Charm quark
• Bottom quark
• Top quark

What Is Beta Decay?

                                                           
Definition: In nuclear Physics, Beta Deacay is the type of radioactive decay, in which an atomic nucleus spontaneously decays into another atomic nucleus to become more stable by emitting an electron ( e− or β− ) or positron ( e+ or β+ ).

In β− decay:

In this subtype of beta decay, no. of neutrons are more than the no. of protons then a neutron turns into proton and makes a new electron e− this electron is not an ordinary electron, 
its a very fast moving electron, And this fast moving electron is Beta Particle. 

Atomic number Z of daughter nucleus is increased by 1, 
while its mass number A remain unchanged,
which is shown as:

                                                                    n → p + e− 

In β−  decay, β− decay generally occurs in neutron-rich nuclei, the weak interaction converts an atomic nucleus into a nucleus with one higher atomic number while emitting an electron (e− ):

A
ZX → A
Z+1Y + e− 

14
6C   → 14
7N + e− 

where A and Z are the mass number and atomic number of the decaying nucleus.

In β+ decay:

In this subtype of beta decay, no. of protons are more than the no. of neutrons, and a proton turns into neutron and makes a new positron e+,this positron is not an ordinary positron, its a very fast moving positron,
And this fast moving positron is Beta Particle. 
Atomic number Z of daughter nucleus is decreased by 1, while its mass number A remain unchanged. In this beta decay, a proton turns into neutron and positron e+ , which is shown as: 

                                                                     p → n + e+ 

In β+ decay, or "positron emission", the weak interaction converts a nucleus into its next-lower neighbor on the periodic table while emitting a positron (e+):

A
ZX → A
Z−1Y + e+  

23 12Mg

→

22 11Na

+

e+

where A and Z are the mass number and atomic number of the decaying nucleus.

When beta decay occurs:

1) when neutrons to protons ratio is above the Band of stability, then  β−  decay occurs.

 As

12

6C → neutron/proton = 6/6 = 1/1 → Its pretty good ratio for stable nuclei which don't go under decay.

14
6C → n/p = 8/6 = 1.33 →Its ratio is big high and nuclei will go under decay.

                                                                      n → p + e− 

Result will be 

14
6C → 14
7N + e−

2) when neutrons to protons ratio is below the Band of stability, then  β+  decay occurs.

As

23

12Mg → neutron/proton = 11/12 = 0.9116 → Its not good ratio and nuclei will go under decay. 

                                                     p → n + e+  

Result will be

23
12Mg → 23
11Na + e+

 

The Electron K.E in the beta decay are found to vary contineously from zero to maximum value as shown by graph. As only 1/3 of max. energy is taken by electron and 2/3 of max. energy seems to be missed.

And we know that law of conservation of energy must hold

in beta decay. This problem was solved by Fermi, who

gave neutrino hypothesis, first suggested by Pauli.

According to this hypothesis, an additional partical

called neutrino ( v ) or antineutrino ( ν ) also created in

beta decaywhich carries away the missing energy. Neutrino has very small mass ( of the order of few ev ) and has charge zero.This hypothesis was confirmed by experiments later.

hence, both energy and momentum ( linear, angular ) are conserved in this decay process. 

On the basis of neutrino hypothesis beta decay process can be written as:

For  β−                                     

                             n → p + e− +  ν

                                                                       14
6C → 14
7N + e− + ν
e

For β+ 

                    p → n + e+ +  v

                                                        23
12Mg → 23
11Na + e+ + v

                                                                                                  10
6C → 10
5B + e+ + v
  

Electron capture (K-capture):

A beta decay occur in which an electron is captured from inner orbits by nucleus, with the result that proton becomes a neutron and a neutrino is emitted as shown:

                                                        p  + e− →  n + v

e.g.

                                   

                                                                          1¹H+ e− →  n + v
The emitted neutrino is mono-energetic. This decay is also called K-capture because the innermost electron of an atom belongs to the K-shell of the electronic configuration of the atom, and this has the highest probability to interact with the nucleus.

What is nuclear force?

It is a force which is responsible for holding the nucleons ( proton and neutron ) in a nucleus and thus making the nucleus stable.

It has four types:
(1). n-n force
(2). p-p force
(3). p-n force
(4). n-p force

Main characteristics of Nuclear Force:-
(1). Nuclear forces are attractive forces and strongest among all the other forces.
(2). Nuclear forces are short range forces.
(3). Nuclear forces are operative within the range of  10¯¹³ cm. 
(4). Nuclear forces are central forces.
(5). Nuclear forces don't obey inverse square law

(6). Nuclear forces are charge independent.
(7). Nuclear forces are spin dependent. e.g.
      A complete of a proton and a neutron with parallel spin form a stable particle (deutron).
(8). Nuclear forces turn into strong repulsive forces when the distance between
       the nucleons becomes smaller as compared with nucleus diameter.

Assumptions:-
(1). The nuclear force ( n-n , p-p , n-p ) are assumed to be almost equal in magnitude and
       independent of charge of nucleons & supported by ( p-p , n-p ) scattering at lower energies.
      This assumption is known as "Hypothesis of charge independence of nuclear forces".
(2). The nuclear forces ( n-n , p-p ) are assumed to be nearly equal and must be smaller
       than ( n-p ) forces & supported by ( p-p , n-p ) scattering at high energies.
       This assumption is known as "Hypothesis of charge symmetry of nuclear forces".

What are scleronomous and Rheonomous constraint?

scleronomous constraint:
constraint that is independent of time. e.g. pendulum of inextensible string. x² + y² = l² equation is independent of time.
Rheonomous constraint:
constraint that contains time explicity. e.g. pendulum of inextensible string. x² + y² = l²(t). where l(t) is the length at time (t).

What are Euler's angles?

The three successive angles of rotation involved when we go from space set of axes to body set of axes. We use three angles  Theta θ, Phi φ, Psi ψ as the generalized coordinates to specify the orientation of rigid body from body set of axes relative to the space set of axes, is known as Euler's angles.

What are inertial and non-inertial frame of references?

Inertial Frame frame of reference is one in which Newton's law hold. i.e   Acceleration = 0
Non-Inertial Frame frame of reference is one in which Newton's law do not hold. i.e   Acceleration ≠ 0

Considering electrons and photons as particles how are they different from each other?

An electron is a negativily chargred particle of spin 1/2. A photon is a neutral particle of spin 1. Electron carry mass. Photon does not carry any mass. Photon travels with the speed of light but electron travels at lesser speed.

Define Briefly Schrodinger equation?

In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of some physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.

Why Are Some Spectral Lines In Hydrogen Spectrum Are Brighter Than Others?

Different Lines Have Different Energy And Hence Different Intensity. Thats Why, Some Spectral Lines Brighter Than Others.

What Is Nuclear Energy?

The energy released during nuclear fission or fusion, especially when used to generate electricity.
Nuclear energy is energy in the nucleus (core) of an atom. Atoms are tiny particles that make up every object in the universe. There is enormous energy in the bonds that hold atoms together. Nuclear energy can be used to make electricity. But first the energy must be released. It can be released from atoms in two ways: nuclear fusion and nuclear fission. In nuclear fusion, energy is released when atoms are combined or fused together to form a larger atom. This is how the sun produces energy.  In nuclear fission, atoms are split apart to form smaller atoms, releasing energy. Nuclear power plants use nuclear fission to produce electricity.

Why Bohr put forward the model of hydrogen atom?

To Explain The Drawbacks Of Rutherford Model, Bohr put forward the model of hydrogen atom.