ALPHA PARTICLE SPECTRUM? - DETAILED EXPLANATION

We have discussed that every alpha(𝛼) emitter has only one associated 𝛼 energy. This is experimentally true for many 𝛼 emitter where one finds that velocity spectrum of alpha particle from these isotopes is always a shar line spectrum. This is to be expected that since the emission of an alpha particle is a result of energy transition between two different nuclear states.

in 1930, S. Rosenblum, in France proved by means of spectograph that the 𝛼 particles from Thc(Bi²¹²), all of which had been thought to have same energy, actually were consisted of number of groups of particles with slightly different energies. The 𝛼 particles form a given radioactive substance were collimated with slits and after deflection thru 180⁰ with strong magnetic field, formed lines on photographic plate.

For example, ₈₄Po²¹⁴ decays to ₈₂Pb²¹⁰ byemitting 4 groups of  𝛼 particles having ranges in air 6.91cm, 7.79 cm, 9.04cm and 11.51cm. These ranges correspond to energies 7.68MeV, 8.28MeV, 9.07MeV & 10.51 MeV respectively.

Another example is decay of ₉₀Th²²⁸. 

₉₀Th²²⁸     →    ₈₈Ra²²⁴ + 𝛼

It comprises of five groups of 𝛼-particles with different energies.

𝛼-particle which is emitted by transformation of excited state of parent nucleus to ground state of daughter nucleus will have maximum energy.

In the above example, out of 5, four groups of  𝛼-particles leave the daughter nuclei in excited state. The fifth group of 5.42MeV 𝛼-rays take one to ground state of daughter nuclei. We can note from figure that excited states of nuclei reach ground state by emitting 𝜸-rays shown by vertical wavy lines.

Thus the fine structure of 𝛼-spectrum tells us about energy levels in daughter nuclei. We emphasize that existence of these different 𝛼-energy groups and 𝜸-rays proves the existence of nuclear energy levels.

Long Range 𝛼-particles:

If the parent 𝛼-emitter emits 𝛼-particles when it is in an excited state, then we get long range 𝛼-particles.  This is because the energy of excitation becomes available to 𝛼-particles as they reach the ground state of daughter nuclei.

The following figure illustrates the emission of long range 𝛼-particles from ₈₄Po²¹⁴.

𝛼ₒ - normal 𝛼-group corresponding to transition between ground states of  ²¹²Po and ²⁰⁸Pb.

𝛼₁, 𝛼₂ - these groups originate from transitions from excited states of parent ²¹²Po to daughter ²⁰⁸Pb directly.

Thus, nuclear spectroscopic studies of long range 𝛼-emitters provide information about nuclear energy levels of parent.

How to set trip point in overload relay of starter?

Well, most of the engineers, who use the motors find sometimes get quizzed that how they should find right trip point on the overload relay in the starter for the motor.

For this, one must find the current rating provided on the motor. This is usually the safe current which the winding of the motor can work with out failure. Usually the winding of motor can withstand high current also based on the time. If the motor curve is available it is easy to find out the required trip current based on the trip time.

or else, one has to consider the 1.5 times of the rated current of motor. When we set the trip point on the relay at the required current, the next step is to ensure the trip time. Trip time could be find out by using equivalent load.

The final step to ensure that you have used the proper relay is to perform rotor lock test
of the motor.        

What is rotor lock test?

The name itself gives and idea that it is locking of the shaft or rotor. One has to lock the rotor and switch on the motor.
This will lead to high current passage through winding. The relay should get tripped within prescribed time by manufacturer
to stop damage to the winding. This is the worse condition of failure and thus, suitable use of relay and trip set point, will always protect the motor.

Any queries are welcome.

Polar Dielectric in Uniform Electric Field

 i) There are permanent dipoles present in Polar Dielectric which are randomly aligned in such a way that there exists permanent dipole moment  Pp.

ii) When a dipole is present in an uniform electric field the dipole tries to align itself in the direction of electric field.

iii) Because of this all dipoles in polar dielectric are partially aligned in the direction of the field. This partial alignment is responsible for the induced dipole moment Pi.

Therefore the electric dipole moment is increasing.

P = Pp + Pi

iv) The electric dipole moment of a polar dielectric increases

      a) by increasing the applied electric field

      b) by decreasing the temperature 

Thermodynamics - important points to be noted for competitive exams

➔ Tephigram is the name of temperature entropy diagram

➔ PV graph in a adiabatic change is called Isentropic.

➔ Entropy of a system is an index of “unavailable energy”.

➔ When gas is expanded, work is done by the gas on surroundings.

➔ The size of “Kelvin degree” is equal to “Centigrade”.

➔ The efficiency of a carnot engine increases by raising the temperature of the source.

➔ Work done per cycle is given by the area enclosed in the indicator diagram.

➔ Conversion of heat energy into electrical energy can be made by “Thermocouple”.

➔ f(P,V,T) =0 exists for an equilibrium state and is called equation of state.

➔ The area of cycle of T-S diagram gives the “available thermal energy for useful work” in a reversible process.

➔ Uses of TS diagram: 

a) used in meteorology b) check efficiency of heat engine c) useful in predicting defects of performance of engine d) to obtain work value of fuel used.

➔ Change in entropy of universe due to free expansion is 
∆S = nR log e(Vf/Vi)

➔ Loss of available of energy = To.dS where ‘To’ is lowest available temperature in system.

➔ In order to maintain a body in an isothermal condition, heat has to be either supplied or withdrawn.

➔ When a gas expands adiabatically, the temperature decreases.

➔ When a gas is compressed, the temperature increases because work is done on the gas.

➔ The work done in an adiabatic change in a particular gas depends upon only change in temperature.

➔ In an adiabatic compression, the decrease in volume is associated with increase in temperature & increase in pressure.

➔ For an isothermal expansion of a perfect gas, the value of dP/P is equal to -dV/V. 

 

➔For an adiabatic expansion of a perfect gas, the value dP/P is equal to -𝛾dV/V.  

 

➔ A reversible process is always “quasi-static”, but every quasi-static process need not be a reversible process.

➔ For reversible cycle: ∆P = ∆V = ∆T = ∆U = ∆H

➔ dW = PdV is only applicable to reversible process. 

➔ In case of “irreversible processes”, dW is not equal to PdV; 

 

➔For free expansion, dW=0

➔For free expansion, dV=0, the work may be zero (in case of PV work)

 

➔ Work and heat are path functions.

➔ Work is not a thermodynamic property as it is not a state function and it is not a exact differential.

➔ Both thermodynamic and temperature scales use a single reference temperature i.e triple point of water.

➔ dW = PdV is only applicable to reversible process. 

➔ In case of “irreversible processes”, dW is not equal to PdV;

Heat Transfer due to conduction

In this mechanism, heat transfer is due to vibration amplitudes of molecules & atoms present in solids.

Consider a cubicle of solid. Let us maintain one face of cube at high temperature (TH) and other opposite face at low temperature(Tc).

Due to temperature difference an amount of heat energy (Q) passes from  hot face to cold face in time 't'.

Conduction rate  Pcond (amount of energy transferred for uni time) is

Pcond = Q/t = K*A*(TH-Tc)/d;

where 'K' is coefficient of thermal conductivity, a constant for given material.
           'd' is thickness of slab
           'A' Area of slab
            't' is time of conduction

Therefore, Q= K*A(TH-Tc)*t/d

Note: i) 'K' depend on nature of material of which slab is made
         ii) A good thermal conductor has 'K' greater value.

Thermal Resistance to conduction(R-value):

This explains resisting of thermal conductivity. The R-value(thermal resistance) of a slab of thickness 'd' is defined as R=d/k. Thus material having less value of 'K' will have higher R-value and thus acts as a good thermal insulator.

Note:

i) 'R' is properly assigned to specified thickness of slab but not to material of slab.
ii) In steady state, conducting rates thru any no. of materials must be equal.
     Therefore, Pcond = A*(TH-Tc) / Σ(d/K)
iii) Heat is transferred from molecule to molecule by conduction. In this case molecules do not bodily move but simply vibrate.