The natural structure provides a blueprint for creating ultra-durable synthetic materials that could be useful for mechanical components in electronics, and in other devices that undergo repetitive movement, abrasion and contact stress.

When a wave undergoes reflection at a denser mediums, Its phase changes at 180^o.

The constituent particles of atom are called sub atomic particles. Therefore electron, proton and neutron are sub atomic particles. Later it was understood that protons and neutrons are made up of quarks. These quarks are also sub atomic particles. Recently it is discovered that the Higgs particles or God particles give mass to many particles like protons, neutrons etc.

One atomic mass unit (u) is defined as the (1/12)^th of the mass of the isotope of carbon \(_{ 6 }^{ 12 }{ C }\)  
\(\mathrm{lu}=\frac{\text { mass of }_{6}^{12} \mathrm{C} \text { atom }}{12}=\frac{1.9926 \times 10^{-26}}{12}=1.660 \times 10^{-27} \mathrm{~kg}\)

(i) Most of the alpha particles are un-deflected through the gold foil and went straight.
(ii) Some of the alpha particles are deflected through a small angle.
(iii) A few alpha particles (one in thousand) are deflected through the angle more than 90^o.
(iv) Very few alpha particles returned back (ie) deflected back by 180^o.

(i) Speed of Electromagnetic wave \(=\frac{Peak\ value\ of\ Electric\ field}{Peak\ value\ of\ magnetic\ field}\)
\(c=\frac { { E }_{ 0 } }{ { B }_{ 0 } } \)
(ii) Yes, As Electromagnetic waves contain both electric and magnetic fields, there is a non-zero energy density associated with it.
\(E=\frac { hc }{ \lambda } \)
Momentum p \(=\frac{Total\ energy\ transferred\ to\ the\ surface}{Velocity\ of\ light\ in\ vacuum}\)
i.e.p = \(\frac{U}{c}=mc\)
U - total energy transferred to the surface.
EM waves carry not only energy and momentum but also angular momentum.

The amplitude of the electric field, E₀ = 3 x 10⁴ NC^-1
The amplitude of the magnetic field, B₀ = 2 x 10^-4 T. Therefore, speed of the electromagnetic wave in a medium is
v = \(\frac { 3\times { 10 }^{ 4 } }{ 2\times { 10 }^{ -4 } } \)  = 1.5 x 10⁸ ms^-1.

Case (a) The position vector for the +q on the positive x-axis is a\(\hat { i } \) and position vector for the +q charge the negative x-axis is - a\(\hat { i } \) So the dipole moment is,
\( \vec { p } =(+q)(a\hat { i } )+(+q)(-a\hat { i } )=0\)
Case (b) In this case one charge is placed at the origin, so its position vector is zero. Hence only the second charge +q with position vector a\(\hat { i } \) contributes to the dipole moment, which is \(\vec { p } =qa\hat { i } \).
From both cases (a) and (b), we can infer that in general the electric dipole moment depends on the choice of the origin and charge configuration. But for one special case, the electric dipole moment is independent of the origin. If the total charge is zero, then the electric dipole moment will be the same irrespective of the choice of the origin. It is because of this reason that the electric dipole moment of an electric dipole (total charge is zero) is always directed from –q to +q, independent of the choice of the origin.
Case (c) \(\vec { p } =(-2q)a\hat { j } +q(2a)(-\hat { j } )=-4qa\hat { j } \) 
Note that in this case \(\vec { p } \) is directed from -2q to +q.
Case (d) \(\vec { p } =-2qa(-\hat { i } )+qa\hat { j } +qa(-\hat { j } )\)
= \(2qa\hat { i } \).
The water molecule (H₂O) has this charge configuration. The water molecule has three atoms (two H atom and one O atom). The centers of positive (H) and negative (O) charges of a water molecule lie at different points, hence it possess permanent dipole moment. The electric dipole moment  \(\vec { p } \) is directed from center of negative charge to the center of positive charge, as shown in the figure.

Advantages of robotics:
(i) The robots are much cheaper than humans.
(ii) Robots never get tired like humans. It can work for 24 x 7. Hence absenteeism in work place can be reduced.
(iii) Robots are more precise and error free in performing the task.
(iv) Stronger and faster than humans.
(v) Robots can work in extreme environmental conditions: extreme hot or cold, space or underwater. In dangerous situations like bomb detection and bomb deactivation.
(vi) In warfare, robots can save human lives.
(vii) Robots are significantly used in handling materials in chemical industries especially in nuclear plants which can lead to health hazards in humans.
Disadvantages of Robotics:
(i) Robots have no sense of emotions or conscience.
(ii) They lack empathy and hence create an emotionless workplace.
(iii) If ultimately robots would do all the work, and the humans will just sit and monitor them, health hazards will increase rapidly.
(iv) Unemployment problem will increase.
(v) Robots can perform defined tasks and cannot handle unexpected situations.
(vi) The robots are well programmed to do a job and if a small thing goes wrong it ends up in a big loss to the company.
(vii) If a robot malfunctions, it takes time to identify the problem, rectify it, and even reprogram if necessary. This process requires signi cant time.
(viii) Humans cannot be replaced by robots in decision making.
(ix) Till the robot reaches the level of human intelligence, the humans in work place will exit.

The atomic weight of lithium
= \(\frac { 7.5\times 6.01512+92.5\times 7.01600 }{ 100 } \)
\(=\frac { 45.1134+648.98 }{ 100 } =6.94093\)

(i) In 1911, Geiger and Marsden did a remarkable experiment based on the advice of their teacher Rutherford, which is known as the scattering of alpha particles by gold foil.

(ii) The experimental arrangement. A source of alpha particles (radioactive material, for example, polonium) is kept inside a thick lead box, with a fine hole.
(iii) The alpha particles coming through the fine hole of the lead box pass through another fine hole made on the lead screen. These particles are now allowed to fall on a thin gold foil and it is observed that the alpha particles passing through gold foil are scattered through different angles.
(iv) A movable screen (from 0° to 180°) which is made up of zinc sulphide (ZnS) is kept on the other side of the gold foil to collect the alpha particles. Whenever alpha particles strike the screen, a flash of light is observed which can be seen through a microscope.
(v) Rutherford proposed an atom model based on the results of alpha scattering. experiment.
(vi) In this experiment, alpha particles (positively charged particles) are allowed to fall on the atoms of a metallic gold foil. The results of this experiment. Rutherford expected the nuclear model, but the experiment showed the model.

(a) Most of the alpha particles were un-deflected through the gold and went straight.
(b) Some of the alpha particles are deflected through a small angle.
(c) A few alpha particles (one in a thousand) are deflected through an angle more than 90°.
(d) Very few alpha particles returned back (backscattered) that is, deflected back by 180°.

(i) \(\lambda =\frac { 2\pi }{ 300\pi } =\frac { 1 }{ 150 } m\)
\([{ B }_{ y }={ B }_{ o }sin2\pi \left( \frac { x }{ \lambda } +\frac { t }{ r } \right) ]\)
(ii) \(\\ { E }_{ o }=c,{ B }_{ o }=3\times { 10 }^{ 8 }\times 8\times { 10 }^{ -6 }=2400{ Vm }^{ -1 }\)

(i) In some AC generators may have more than one coil in the armature core and each coil producesan alternating emf. In these generators, more than one emf is produced.  Thus, they are called poly-phase generators.
(ii) If there are two alternating emfs produced in a generator, it is called two-phase generator, it is called two-phase generator. In some AC generators, there are three separate coils, which owould give three separate emfs. Hence, they are called three-phase AC generators.
(iii) In the simplified construction of three-phase AC generator, the armature core has 6 slots, cut on its inner rim. Each slot is 60° away from one another. Six armature conductors are mounted in these slots.The conductors 1 and 4 are joined in series to form coil 1. The conductors 3and 6 form coil  2 while the conductors 5 and 2 form coil 3. So, these coils arerectangular in shape and are 120° apart from one another.
(iv) The initial position of the field magnet is horizontal and field direction is perpendicular to the plane of the coil 1. As it is seen in single phase AC generator, when field magnet is rotated from that position in clockwise direction, alternating emf ε₁ in coil 1 begins a cycle from origin O. This is shown in Figure.

(v) The corresponding cycle for alternating emf ε₂ in coil 2 starts at point A after field magnet has rotated through 120°. Therefore, the phase difference between ε₁ and ε₂ is 120°. Similarly, emf ε₃ in coil 3 would begin its cycle at point B after 240° rotation of field magnet from initial position. Thus these emfs produced in the three phase AC generator have 120° phase difference between one another.

v = nג
In an isotropic medium, there is no change in the frequency of the light. So, the speed of light depends on wavelength of light.

(i) Nano-robots in blood stream to perform small surgical procedures, to fight against bacteria, repairing individual cell in the body.
(ii) It can travel into the body and once after the job is performed it can find its way out. Chinese scientists have created the world's first autonomous DNA robots to combat cancer tumours.

Atomic mass unit is defined as \(\frac{1}{12}\) ^th of the mass of one \(_{ 6 }^{ 12 }{ C }\) atom.
E = mc²
= 1.66 x 10-27 x 3 X 108 x 3 x 108 J
= 1.66 x 9 x 10-11 J
= \(\frac { 1.66\times 9\times { 10 }^{ -11 } }{ 1.6\times { 10 }^{ -13 } } \) MeV = 931 MeV.

Current lags behind the applied voltage by \(\frac{\pi}{2}\) in an inductive circuit.