13.2.3 - 13.2.4

13.2.3
The nucleus, as a quantum system contains discrete energy levels. Alpha particles have discrete energies along with the gamma ray spectra. Quantum energy being emitted from both are quantized and discrete, only having certain values, and showing that the nucleus itself has discrete nuclear energy levels.

13.2.4
The beta energy spectra is continuous and was not understood before the postulation of the neutrino. As scientists were investigating they discovered that the beta particles had three times less emissions than what was predicted, undermining the basic principles of physics (conservation of energy.) This led to the postulation of the Neutrino. A particle that was almost undetectable and that carried away the missing kinetic energy and momentum present in the reaction. It is neutral with a minute mass, travelling at the speed of light.

During positron decay a proton contained within the nucleus decays into both a neutron and a positron, which are then emitted. Due to neutrinos and anti-neutrinos, the beta emissions form a continuous spectra.

19.3
Work Function = 3.413E-19

19.4
KE Max = hf - WFunction
=6.6E-19 * 3.2E-9 - 3.41E-19
=3.8E-19
KE = qStoppingVoltage
Vs = 3.8E-19/me=3.8E-19/91E-31
4.2eV

19.5
2.4E-19 - 3.6E-19 = -WFunction
Work Function = 1.56E-19

Induced Electro-Motive Force.

12.1.1: 

Emf is the amount of mechanical energy converted into electrical energy per unit charge. The unit of an induced emf is the volt. This happens when the free charges moving in a magnetic field are contained within a conductor. This is affected by the rate of flux cutting (Also just v for the velocity the conductor moves through the field), B - field of flux density and L, the length of the conductor itself. The optimal angle for a conductor to flux cut is perpendicular to the magnetic field lines.

12.1.2:

FB= FE

FB= BeV

E = -dV/dx = V/L

FE = Ee = Ve/L

Ve/L = BeV

V=BLV

12.1.3: 

Faraday's law shows that the induced emf is equal to the rate of change of flux. This is due to the fact that the different variables, flux density, speed of movement and length of the conductor change at the rate which the conductor cuts through the magnetic field lines. This applies to all examples of induced emfs.

12.1.4:

This happens mainly during AC power production, where the power is sent primarily to the coil causing a change in the magnetic field in the transformer. Transformer-induced emf is induced by a time-changing magnetic flux, namely a wire in a magnetic field that changes with time. 

12.1.5:

Faraday's: Total flux linkage is given by NФ. The rule governing induced emf can be stated as the magnitude of an induced emf being proportional to the rate of change of flux linkage. emf = N(ΔФ/Δt)

Lenz's: The direction of an induced emf opposes the change which caused it. For example if a current was induced downwards the force would be upwards. The original motion would be opposed.

Questions:

39. 

a) 

Emf = BLV

50x10^-6 x 0.2 x 20

= 2x10^-4 v

b)

R = 2

I=V/R

=2x10^-4/2

=1x10^-4 a

c)

I^2R

=2x10^-8 w

d)

2x10^-8 w

e)

20 meters in one second.

f)

w=fxd

f = w/d

f=2x10^-8 / 20 = 1x10^-9 N

40.

a)

AxB

2x10^-4 x 100 x 10^-6

=2x10^-8

=50x2x10^-8

=1x10^-6

b)

Since flux changed density to 50 then flux enclosed is 0.5x10^-6

ΔB/Δt = 1.0 – 0.5 / 2

=0.25 MTm^-2s^-1

 c)

Induced emf = rate of change of flux = 0.25 MV