Quantum Physics

Question 1

What is photoelectric effect?

Answer 1

Photoelectric effect refers to the emission of electrons from a metal surface when electromagnetic (EM) radiation of sufficiently high frequency is incident on it.

Question 2

What are the 4 major observations of photoelectric effect?

Answer 2

4 Major Expt Observations of PE:

(a) No electrons are emitted if the frequency of the EM radiation is below a minimum frequency {called the threshold frequency fo}, regardless of the intensity of the radiation.
(b) Photoelectric current is proportional to the intensity of radiation, for a fixed frequency (because the rate of emission of electrons ∝ rate of incidence of photons)
(c) Max KE of photo-electrons depends only on the frequency and the work function, of the metal used, not the intensity. {Note: Emitted electrons have a range of kinetic energy, ranging from zero to a certain maximum value}
(d) Emission of electrons begins instantaneously {i.e. no (measurable) time lag between emission & illumination} even if the intensity is low.

Question 3

What are the contradictions between classical wave theory and photoelectric effect?

Answer 3

(a) No electrons are emitted if the frequency of the EM radiation is below a minimum frequency
{called the threshold frequency fo}, regardless of the intensity of the radiation.
(b) Max KE of photo-electrons depends only on the frequency and the work function, of the
metal used, not the intensity.
{Note: Emitted electrons have a range of kinetic energy, ranging from zero to a certain
maximum value}
(c) Emission of electrons begins instantaneously {i.e. no (measurable) time lag between emission
& illumination} even if the intensity is low.

Question 4

What is the defintion of a photon?

Answer 4

A photon is a discrete packet {or quantum} of energy of an electromagnetic radiation with energy hf.

Question 5

What is the formula for energy of a photon?

Answer 5

E = hf = hc/λ

Question 6

What are the wavelength of violet light and red light?

Answer 6

violet: 4 x 10-7 m
red: 7 x 10-7 m

Question 7

What is the photoelectric equation?

Answer 7

energy of a photon = work function + max. KE of ejected electrons
hf = Ø + 1⁄2 mev2 max

Question 8

What is threshold frequency and work function?

Answer 8

Threshold frequency fo is the minimum frequency of the EM radiation required to eject an electron from a metal surface.
Work function of a metal is the minimum energy required to eject an electron from a metal surface.
{This energy is necessary because the electrons are held back by the attractive forces of the positive nuclei in the metal.}

Question 9

What is stopping potential?

Answer 9

Stopping potential Vs is the minimum negative potential required to stop the fastest electron {& thus, ALL the electrons} from arriving at the collector plate.

Question 10

What is the formula for maximum KE of electrons?

Answer 10

Maximum KE of electrons, 1⁄2 mev2max = eVs, where Vs : stopping potential

Question 11

Why do electrons have a range of KE?

Answer 11

electrons below the surface lose some KE on their way to the surface if and when they collide with the metallic lattice. They do not ALL experience the same loss in KE during such collisions before they are emitted. Hence the KE of the emitted electrons has a range of values.

Question 12

What is the graph of photoelectric current and intensity at constant frequency?

Answer 12

Straight-line graph passing through point of origin.
As intensity increases, number of incident photons per unit time on the emitter increases hence more photoelectrons are emitted per unit time. Thus current increases proportionately.

Question 13

What is the graph of photoelectric current against p.d. across emitter and collector?

Answer 13

x

Question 14

What happens when intensity doubles without changing frequency?

Answer 14

If intensity doubles, without changing frequency,

1) saturation current doubles
2) stopping potential Vs: no change

Question 15

What can’t current increase beyond it ‘saturation value’ when p.d. increases?

Answer 15

For that given light intensity, all electrons ejected by the photons are already successfully attracted to the collector even for a low positive voltage applied {i.e. none has managed to “escape” through the sides of the photo cell}; thus increasing to a higher positive V value will not increase the current which is proportional to the number of electrons collected per unit time.)

Question 16

What does the sloping section of the graph represent?

Answer 16

It denotes the fact that the electrons are emitted with a range of KE.

Question 17

What is graph eVs against frequency? Gradient? Vert./horiz. intercept?

Answer 17

Linear graph with negative vert-intercept - Ø. & gradient = h
Horizontal Intercept = f0
Deduced from: eVs = hf − Ø.

Question 18

What is formula of intensity?

Answer 18

Intensity = Power/Illumintated Area = Ephotons/At = nhf/At

Question 19

Why is rate of emission of electrons much smaller than rate of incidence of photons?

Answer 19

1. Not every photon would collide with & emit an electron; most are reflected by the metal or miss hitting any electron.
2. On the way out to the metal surface, an electron may lose some kinetic energy to ions and other electrons it encounters along the way. This energy loss prevents it from overcoming the work function & so such electrons are absorbed by the metal.

Question 20

What is wave-particle duality?

Answer 20

It refers to the idea that light and matter {such as electrons} have both wave & particle properties.
Interference and diffraction provide evidence for the wave nature of E.M. radiation.
In contrast, photoelectric effect provides evidence for the particulate nature of E.M. radiation.
These evidences led to the concept of the wave-particle duality of light.
Electron diffraction provides evidence that matter /particles have also a wave nature & thus, have a dual nature.

Question 21

What is the formula for de Broglie wavelength of a particle?

Answer 21

λ = h/mv = h/p

Question 22

What are energy levels? Characteristics?

Answer 22

It refer to the possible energy values an electron can have without it radiating any
energy.
1.Energy levels are discrete/ quantised {i.e. can only have certain energy values}.
2.Energy difference between successive energy levels in an energy level diagram, ΔE, decreases as we
move from ground state upwards.

Question 23

What is isolated atom?

Answer 23

It refers to an atom whose nearest neighbouring atom is sufficiently far apart that the inter-atomic force between them is negligible. Eg. A low density monatomic gas (i.e. a gas at low pressure). Such atoms will produce a line spectrum, not continuous spectrum.

Question 24

What is ionisation energy?

Answer 24

Ionisation energy is the minimum energy required to remove an unexcited electron from the atom

Question 25

How to excite an atom?

Answer 25

1. a bombarding particle (typically, an electron): only if the bombarding electron has KE ≥ ΔE
   (difference in energy levels)
2. absorption of an incident photon: can occur only if energy of photon is exactly equal to ΔE

Question 26

What is energy of absorbed photon?

Answer 26

Energy of the absorbed (or emitted) photon is = difference in energy between these 2 energy
levels/states: ∆E = |Ef − Ei| = hf = hc/λ

Question 27

What is emission line spectrum?

Answer 27

A series of discrete/separate bright lines of definite wavelength/frequency on a dark background.
It is produced by electron transitions within an atom from higher to lower energy levels and emitting photons.

Question 28

What is absorption line spectrum?

Answer 28

A continuous bright spectrum crossed by “dark” lines (due to some ‘missing’ frequencies).
It is produced when white light passes through a ‘cool’ gas. Atoms/electrons of the cool gas absorb photons of certain frequencies from the white light source, and get excited to a higher energy level which are then quickly re-emitted uniformly in all directions.

Question 29

How does existence of electron energy levels in atoms give rise to line spectra?

Answer 29

Energy levels are discrete.

1. During a downward transition, a photon is emitted.
2. Frequency of photon, f = Ei - Ef / h
3. Since Ei & Ef can only have discrete values, the frequencies are also discrete and so a line {rather than a continuous} spectrum is produced.

Question 30

What are the significance of line spectra?

Answer 30

1. The fact that the lines are separated/ discrete is experimental evidence for the existence of discrete or “quantized” energy levels in the atoms.
2. Because all isolated atoms of any particular element have the same characteristic set of energy levels, each element produces a unique line spectrum which may be used to identify the element (source of the radiation).

Question 31

What are the 3 feature of X-ray spectrum?

Answer 31

characteristics lines, continuous background, minimum wavelength.

Question 32

What are characteristic X-rays?

Answer 32

1. A high-energy electron colliding with a target metal atom may knock an electron out of an inner shell of the target metal (thus creating a vacancy).
2. Another electron (of target atom) from a higher energy state then drops down to fill the vacancy, thus emitting an X-ray with a specific wavelength, which is determined only by the difference in energy betw the 2 energy levels (which are characteristic of the target metal).
   We can deduce: frequency of characteristic x-ray is independent of the accelerating voltage
   (i.e. operating p.d.) V, but dependent on the target element.

Question 33

What is continuous X-ray spectrum?

Answer 33

Such x-rays are produced when fast electrons are suddenly decelerated upon colliding with atoms of the metal target.
1. The frequencies of emitted X-rays have a continuous range because the decelerations can occur in a nearly infinite number of different ways &
2. hence the energies lost by electrons vary from one collision to another across a continuous range of values (hence spectrum). {The freq of the X-ray emitted after each collision is determined by the loss in KE of the decelerated electron for that collision.}
WE can deduce: frequencies of continuous spectrum depends on the accelerating voltage (i.e. operating p.d.) V.

Question 34

What is the minimum wavelength of continuous spectrum? What is the formula?

Answer 34

When a bombarding electron loses all of its kinetic energy (derived from work done by the accelerating voltage, eVa) due to a single collision with the target metal, an X-ray photon of the highest energy (and therefore minimum wavelength) is produced.
eVa = hc/λmin
Va = accelerating voltage (applied across the X-ray tube)
λmin is the wavelength of the X-ray photon emitted when a bombarding electron loses ALL its KE in a single collision with the target atom.
Thus the minimum wavelength depends on the voltage applied across the X-ray tube.
Common mistake: is to apply the deBroglie wavelength λ = h/mev to determine λmin of X-rays.

Question 35

What is Heisenberg’s uncertainty principle? What is the formula?

Answer 35

If a measurement of the position of a particle (typically an electron) is made with uncertainty Δx and a simultaneous measurement of its momentum is made with uncertainty Δp, the product of these 2 uncertainties can never be smaller than h.
Δx Δp ≳ h or me Δv Δx ≳ h
A reasonable estimate of Δx = the full length of the “container”.