Quantum Physics Part 1

Question 1

Describe photoelectric effect

Answer 1

Phenomenon where e- r emitted fr metal surface when e-magnetic rad n of sufficient high f is incident on surface

Question 2

Define electromagnetic radiation

Answer 2

exists as discrete bundles (quanta) of energy aka photons

Question 3

Define photon

Answer 3

A discrete bundle/quantum of e-magnetic energy

Question 4

Give formula for energy of photon

Answer 4

energy, E = hf = hc/λ (c=fλ)

where
h is Planck constant (6.63e-34 J s),
f is frequency,
c is speed of light in vacuum (3.00e8 m s-1),
λ is wavelength

Question 5

Describe photon’s characteristics

Answer 5

• only dependent on f
• for given f, beam of EM rad n of greater intensity simply hv more photons per unit time
• changing intensity and photon per unit time no affect whether e- can be emitted

Question 6

Give formula for intensity of a beam of EM radiation

Answer 6

Intensity I = P/A = Etotal/(tA) = NE/(tA )= Nhf/(tA) = nhf

Units: W m-2 or J s-1 m-2

where
E is energy of 1 photon,
N is no of photon,
N/t is rate of incident photon,
n is no of photon passing unit area per unit time

Question 7

What to take note about photons bombarding metal surface?

Answer 7

• 1 e- can oni absorb 1 photon (1:1 ratio)
• not every incident photon cause e- be emitted (due to various factors)
• transfer of energy is immediate (no time delay)

Question 8

Give Einstein’s photoelectric equation

Answer 8

hf = Φ + Ek,max

where
hf is photon energy,
Φ is work funct n energy (of material),
Ek max is max kinetic energy of emitted e-

Question 9

Define work function energy Φ of a material. What to take note?

Answer 9

Φ is min amt energy needed to remove e- fr surface of material

*Φ is a material property (ie diff metal hv diff value)

Question 10

Define threshold frequency, f0 and give formula

Answer 10

f0 is min frequency of incident rad n for e- to escape

f0 = Φ/h

Question 11

Discuss how the photoelectric effect provides evidence for the particulate nature of electromagnetic radiation

Answer 11

1. Existence of threshold frequency below which no photoe- r emittef prove EM rad n consist og discrete quanta of energy given by hf
2. Instantaneous emis n of photoe- when all photon energy is transferred immediately to e- in single collis n give evidence to particulate nature of EM
3. Max Ek of photoe- being dependent oni on f of rad n, relating to discrete energy of photon, & independent on intensity of rad n oso give evidence for particulate nature of EM

Question 12

What is stopping potential?

Answer 12

Min retarding potential (diff) to stop all emitted e- fr reach collector plate

Question 13

Using stopping potential, what formula can be made?

Answer 13

Ek,max = 0.5m(v max)² = e(Vs)

where
Ek max is Ek of e- converted to electric PE,
e is charge of electron,
Vs is stopping potential

Question 14

How to get stopping potential against frequency graph?

Answer 14

hf = Φ + Ek, max
hf = Φ + e(Vs)
e(Vs) = hf - Φ

Thus, Vs = (h/e)f - Φ/e

Question 15

Give photoelectric equations

Answer 15

f = c/λ
hf = Φ + Ek,max
hf0 = Φ
Ek,max = 0.5m(v max)² = e(Vs)

Question 16

Explain photoelectric graphs

Answer 16

1. Vs against f of EM rad for three diff metal (same grad, diff f intercept)
   - recall Vs = (h/e)f - Φ/e
   - threshold f diff bcos diff work funct n of metals
   - slope const as given by h/e (const)
2. current I against intensity (origin straight positive grad line)
   - photocurrent I (rate emis n photoe-) proportional to intensity of EM rad n (rate photon incident); straight line graph obtained (assuming const f and f > threshold f)
3. Photocurrent I against potential of collector plate V (start fr same pt in -ve V axis but Q rise until twice high as P just after passing V=0)
   - consider graph due to 2 light beam of same wavelength, but diff intensity. Q high intensity, P low intensity
   - stopping potential Vs is same due to light beam low intensity P & high intensity Q, since photon energy (& thus Ek,max) is same
   - beam of high intensity Q produce more e- than low intensity P (if Q double P in intensity, current I oso double)
   * assume probability of photoe- emis n const

Question 17

How to convert between Joules and Electron-volts?

Answer 17

1eV = 1.6E-19 J

Question 18

Give de Broglie formula

Answer 18

λ = h/p = h/mv

where
λ is wavelength,
h is Planck const,
p (=mv) is momentum of particle

Question 19

Give two formulae for kinetic energy

Answer 19

Ek = 0.5mv² = p²/(2m)

Question 20

Name evidence showing wave-particle duality of light and electrons

Answer 20

• light as wave: interference/diffraction
• light as particle: photoelectric effect
• electron as particle: e- undergo collis n, hv mass & charge
• electron: e- diffract n

Question 21

Give formula for magnitude of energy change during transition of electron from one energy level to another (emission or absorption of photons)

Answer 21

ΔE = E higher - E lower = hf

where
E higher is higher energy level,
E lower is lower energy level,
hf is energy of emiited/absorbed photon

Question 22

Describe all key features of energy-level diagram

Answer 22

1. n represent quantum no. (oni take integer, discrete value fr 1 to infinity)
2. Ground state refer to lowest energy lvl in which atom is most stable. e- normally occupy this lvl unless given suff energy move up higher lvl
3. highest energy lvl n=infinity correspond to energy state whereby e- no longer bound to atom (ie escaped atom, recall gravitation). By convent n, assigned value 0 eV
4. lower energy lvl, more -ve value associated w that lvl. So, lower energy states correspond to more stable state
5. energy diff btw any 2 adj lvl get smaller as n increase (so higher energy lvl become practically continuous at as n approach infinity)
6. ionisat n energy of atom is energy needed remove orbital e- completely fr atom (ie transit n fr ground state to n = infinity)
7. transit n btw diff energy lvl represented by arrow (relative length of arrow relate to amt energy absorbed/emitted when e- transits btw energy lvl)

Question 23

What must happen during transition between energy levels (or allowed orbits)?

Answer 23

atom can oni absorb (more to higher energy lvl) or emit (drop to lower energy lvl) energy in fixed amt equal to diff btw energy lvl

Question 24

Describe excitation

Answer 24

• an atom said to b excited state when e- found in higher energy lvl (transit n to higher energy lvl)
• there are 2 mechanisms:

1. Absorp n proton
   - energy of photon MUST b exactly equal energy diff btw 2 energy lvl b4 absorbed
   ie. ΔE = E higher - E lower = hf
   Otherwise, not absorbed by e- at ALL
2. high speed collis n by another particle
   - Ek of colliding particle must b >= energy diff btw 2 energy lvl (no need match)
   - colliding particle transfer part of its energy to e- for excitat n (equal to diff btw 2 energy lvl), while keeping rest

Question 25

Describe de-excitation

Answer 25

• transit n of e- to lower energy lvl
• atom can de-excite oni thru 1 mechanism: e- of atom lose exact amt energy by emitting photon of exact f OR λ
  ie. ΔE = E higher - E lower = hf = hc/λ

Question 26

Describe emission line spectrum

Answer 26

• consists of discrete bright coloured lines in dark background

Question 27

Explain how an emission spectrum is produced

Answer 27

• gases eg H, Ne, can b places in discharge tube low Pa. High voltage applied btw metal electrodes in tube large enough to produce current in gas. Gas atoms bcome excited by collis n w e- passing thru tube, fr cathode to anode of discharge tube
• excited gas atom r unstable, transits to lower energy lvl by emit photon
• since atom hv discrete energy lvl, oni specific high-to-low energy lvl transit n r possible, so photon emitted of specific energy, f
• so, coloured lines in emiss n spectrum correspond to emitted photon of specific f

Question 28

Describe absorption line spectrum

Answer 28

consist of dark lines against continuous spectrum of white light

Question 29

Explain how absorption spectrum is produced

Answer 29

• produced when white light pass thru cold gas
• gas atoms r excited to higher energy lvl when absorb photon fr white light
• since atom hv discrete energy lvl, oni specific low-to-high energy lvl transit n possible, so photon absorbed of specific energy, f
• when atom transit back to ground state, photon of same f re-radiated but in all direct n
• so, parts of absorpt n spectrum corresponding to f appear as dark lines as compared to other non-absorbed f

Question 30

Describe how line spectra can be explained using the idea of discrete energy levels in isolated atoms

Answer 30

• each line correspond to specific photon energy
• photon emitted when e- make transit n fr higher to lower energy lvl
• since photon energy is of specific value, implies that energy change btw energy lvl is of discrete amt
• discrete energy change thus implies energy lvl discrete

Question 31

Explain why energy levels of hydrogen atom are labelled negative

Answer 31

• e- & nucleous form bound system, where force btw e- & nucleus is attractive
• since potential at infinity defined to b zero, energy lvl closer to nucleus is lower, so more -ve