Quantum Physics Part 2

Question 1

Describe X-rays are produced in an X-ray tube

Answer 1

step 1: cathode heated to high temp, so emit e-
step 2: cathode, anode hv accelerating potential, so e- accelerate thru pd several thousand volts, acquire vv high Ek
step 3: e- strike metal target embedded in anode. loss Ek in e- converted into high energy EM rad n aka X-ray

Question 2

Explain continuous X-ray spectrum

Answer 2

• e- fr cathode w initial high Ek, i collide w target atom nucleus in anode
• as e- approach nucleus in target atom, it deflects due to attractive force btw nucleus & e-, so e- Ek reduced to Ek,f due to large decelerat n
• loss in Ek converted into EM energy as X-ray photon of energy hf

Ek,i = Ek,f + hf

• photon energy released depend on mag accelerat n (closer e- approach nucleus, larger deflect force so higher energy emitted photon)
• as numerous e- fr cathode strike target, deflect n occur at range of proximities => distribut n photon energies, so wide range of wavelengths, forming continuous spectrum
• since product n X-ray rad n is due to slow down incident e-, so aka ‘braking radiat n’
• if e- still retain some Ek, it continue collide w other target atom, cause more X-ray emis n

Question 3

Explain existence of minimum wavelength, λmin

Answer 3

• there is sharply defined λmin, correspond to max energy X-ray photon, caused by collis n in which incident highly energetic e- stops abruptly in single collis n, all Ek of e- converted into single X-ray photon

max photon energy = complete Ek loss of fastest e-
hc/λmin = Ek,i

• λmin thus affected by accelerating potential
• since e- accelerated by e- field btw cathode, anode, increasing accelerating potential increase max Ek of e-
  => λmin decrease

hc/λmin = Ek,i = e(ΔV)

Question 4

Describe some key characteristics of intensity-wavelength graph of characteristic X-rays

Answer 4

Graph, Kb < Ka, Lb < La

• since Kb de-excit n cause highest E photon, hv shortest wavelength, so La hv longest wavelength
• since e- in L shell closer to K shell, prob that vacancy in K shell filled by e- fr L shell higher than fr M shell
  => rate emis n Ka photon > rate emis n Kb photon
  =>intensity of Ka line relatively higher than Kb line
• since E diff btw discrete E lvl r characteristics of target atom, wavelengths of Ka, Kb characteristic X-rats r unique to each element

Question 5

Give Heidenberg Uncertainty Principle

Answer 5

ΔpΔx >= h

where
Δp is uncertainty of momentum,
Δx is uncertainty of pos n,
h is Planck’s constant