Topic 3: Light and atoms

Convert every energy to joules or every energy to electronvolts before you subtract a work function or compare levels.

Written questions

Measuring a laser's wavelengthWritten question · 7 marks

Students shine a red laser through a double slit with a slit separation of 0.250 mm. For each distance L from the slits to the screen, they use a ruler marked in millimetres to measure the width of five fringe spacings, from the centre of one bright fringe to the centre of the sixth. The table shows their results.

Width of five fringe spacings measured at five slit-to-screen distances, slits 0.250 mm apart.
Slit-to-screen distance L (m)	Width of five fringe spacings (mm)
1.00	12.6
1.50	19.1
2.00	25.2
2.50	31.8
3.00	37.9

(a) A graph of fringe spacing Δy (in metres) against L is a straight line through the origin. Calculate its gradient, using the data in the table. [3]

(b) Calculate the wavelength of the laser light, in nanometres, from your gradient. [2]

0 words · a sentence or two

Planck's constant from stopping voltagesWritten question · 8 marks

A student shines light of five different frequencies, one at a time, on the same metal surface in a photocell. For each frequency she increases the reverse voltage until the photoelectric current just stops, and records this stopping voltage. The table shows her results. Take e = 1.60 × 10⁻¹⁹ C and 1 eV = 1.60 × 10⁻¹⁹ J.

Stopping voltage measured for light of five frequencies falling on the same metal surface.
Frequency (×10¹⁴ Hz)	Stopping voltage (V)
6.0	0.42
7.0	0.82
8.0	1.25
9.0	1.65
10.0	2.08

(a) A graph of stopping voltage against frequency is a straight line. Calculate its gradient, in volt seconds. [2]

V s

(b) Calculate Planck's constant from your gradient. [2]

J s

(d) Another student predicts that a brighter lamp with the same frequencies would give larger stopping voltages. Explain whether the prediction is correct. [2]

0 words · a sentence or two

Electrons diffracted by a crystalWritten question · 6 marks

De Broglie proposed that a moving particle has a wavelength λ = h/p. Davisson and Germer later fired a beam of electrons, accelerated from rest through 54 V, at a nickel crystal. They found a strong reflected beam at one particular angle, at the angle expected for waves diffracted by the regular rows of atoms in the crystal, whose spacing is about 2 × 10⁻¹⁰ m. Take h = 6.63 × 10⁻³⁴ J s, e = 1.60 × 10⁻¹⁹ C and mₑ = 9.11 × 10⁻³¹ kg.

(a) Calculate the de Broglie wavelength of the electrons in the beam. [3]

(b) Explain how this result supported de Broglie's proposal that particles such as electrons have wave properties. [3]

0 words · about 50 to 80 words

Light from a hydrogen lampWritten question · 7 marks

A hydrogen discharge lamp is viewed through a spectroscope, which shows a set of separate coloured lines. The table gives energy levels of a hydrogen atom. Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

(a) Calculate the frequency of the photon emitted when an electron moves from n = 4 to n = 2. [2]

(b) Calculate the wavelength of this light, in nanometres. [2]

0 words · about 50 to 80 words

How a fluorescent tube makes visible lightWritten question · 5 marks

In a fluorescent tube, electrons collide with mercury atoms in a low-pressure vapour and excite them. The mercury atoms emit mainly ultraviolet light of wavelength 254 nm. A phosphor coating on the inside of the glass absorbs this ultraviolet light and emits visible light. Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

(a) Calculate the energy, in electronvolts, of one photon of the ultraviolet light. [2]

(b) Explain why the light emitted by the phosphor has a longer wavelength than the ultraviolet light it absorbs. [3]

0 words · about 50 to 80 words

Annihilation in a PET scannerWritten question · 7 marks

In positron emission tomography (PET), a patient receives a tracer that emits positrons. Each positron travels a very short distance, slows almost to rest and annihilates with an electron. Two photons of equal energy leave the point of annihilation and are detected at the same moment by a ring of detectors around the patient. Take mₑ = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.

(a) Calculate the energy of each photon. [2]

(b) Calculate the wavelength of each photon. [2]

0 words · about 50 to 80 words

Overlapping orders of a white-light spectrumWritten question · 6 marks

White light, with wavelengths from 400 nm to 700 nm, falls at right angles on a diffraction grating with 600 lines per millimetre. Each order beyond the central maximum is a spectrum from violet to red.

(a) Calculate the angle of the red end (700 nm) of the second-order spectrum. [2]

(b) Calculate the angle of the violet end (400 nm) of the third-order spectrum. [2]

0 words · a sentence or two

Checking a sigma decayWritten question · 6 marks

A sigma-minus baryon (Σ⁻), made of two down quarks and one strange quark, decays into a neutron (one up and two down quarks) and a negative pion (π⁻), made of a down quark and an anti-up antiquark. Quark charges: up +⅔e, down −⅓e, strange −⅓e.

(a) Calculate the charge of the Σ⁻, in units of e. [1]

(b) Show that baryon number is conserved in this decay. [3]

0 words · about 50 to 80 words

0 words · a sentence or two

Quick checks: four-option questions

The SACE examination has no multiple-choice questions. These quick checks practise the same physics.

Question 1

Two light sources are described as coherent. Which statement must be true of them?

Question 2

Electrons in a transmitting antenna in the Adelaide Hills oscillate at a frequency of 104.7 MHz. What is the wavelength of the radio waves the antenna emits? Take c = 3.00 × 10⁸ m s⁻¹.

Question 3

Which statement correctly describes the electric and magnetic fields in an electromagnetic wave travelling through a vacuum?

Question 4

Red light of wavelength 633 nm from a laser passes through two narrow slits 0.250 mm apart. The fringes form on a wall 2.40 m from the slits. What is the distance between neighbouring bright fringes?

Question 5

In a two-slit experiment with light of wavelength 600 nm, point X on the screen is at the centre of the second dark fringe from the central bright fringe. What is the path difference between the waves from the two slits that reach X?

Question 6

Yellow light of wavelength 589 nm from a sodium lamp falls at right angles on a diffraction grating with 600 lines per millimetre. At what angle from the straight-through direction is the first-order maximum?

Question 7

A red laser of wavelength 650 nm shines at right angles onto a diffraction grating with 500 lines per millimetre. What is the highest order of maximum that can form?

Question 8

White light falls at right angles on a diffraction grating. Each first-order maximum is a spectrum of colours. Which colour in that spectrum is farthest from the central maximum?

Question 9

In a two-slit experiment the slit separation is halved and the screen is moved to twice its original distance from the slits. The wavelength is unchanged. By what factor does the fringe spacing change?

Question 10

A two-slit pattern made with red light is viewed on a screen. The red light is replaced by blue light, with the slits and screen unchanged. How does the pattern change?

Question 11

A student measures a two-slit pattern on a screen 3.00 m from slits 0.400 mm apart. From the centre of the first bright fringe to the centre of the eleventh bright fringe in a row, the distance is 42.0 mm. What is the wavelength of the light?

Question 12

Laser light falls at right angles on a grating with 300 lines per millimetre. The second-order maxima are measured at 21.1° on each side of the central maximum. What is the wavelength of the light?

Question 13

Light of one wavelength passes first through two slits, then through a grating with the same slit spacing but thousands of slits. How do the grating's maxima compare with the two-slit fringes?

Question 14

Two coherent light waves of equal amplitude meet at a point. One has travelled exactly half a wavelength farther than the other. What is seen at that point?

Question 15

A blue light-emitting diode emits light of wavelength 450 nm. What is the energy of one photon of this light? Take h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.

Question 16

A green laser pointer emits light of wavelength 532 nm. What is the momentum of one of its photons? Take h = 6.63 × 10⁻³⁴ J s.

Question 17

Violet light of wavelength 400 nm falls on a clean sodium surface with a work function of 2.28 eV. What stopping voltage is needed to stop the fastest photoelectrons? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 18

A copper surface has a work function of 4.70 eV. What is its threshold frequency? Take h = 6.63 × 10⁻³⁴ J s and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 19

Ultraviolet light of one frequency, above the threshold frequency, shines on a zinc plate and releases photoelectrons. The light is made twice as intense, with its frequency unchanged. What happens?

Question 20

A student measures the maximum kinetic energy of photoelectrons from a metal for several frequencies of light. The graph shows her line of best fit. What value of Planck's constant does the graph give? Take 1 eV = 1.60 × 10⁻¹⁹ J.

Question 21

A dental X-ray tube accelerates electrons through a potential difference of 25.0 kV. What is the maximum frequency of the X-rays it produces? Take e = 1.60 × 10⁻¹⁹ C and h = 6.63 × 10⁻³⁴ J s.

Question 22

The filament current in an X-ray tube is increased while the accelerating voltage stays the same. How does the X-ray output change?

Question 23

An electron moves at 2.50 × 10⁶ m s⁻¹. What is its de Broglie wavelength? Take h = 6.63 × 10⁻³⁴ J s and mₑ = 9.11 × 10⁻³¹ kg.

Question 24

Davisson and Germer fired a beam of electrons at a nickel crystal and found strong reflection only at certain angles. What did this show?

Question 25

A photon and an electron have the same wavelength of 0.20 nm. How do their momenta compare?

Question 26

A red laser pointer emits light of wavelength 650 nm with a power of 5.00 mW. How many photons does it emit each second? Take h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.

Question 27

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

The table gives energy levels of a hydrogen atom. What is the wavelength of the photon emitted when the electron moves from n = 3 down to n = 2? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 28

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

The table gives energy levels of a hydrogen atom. An atom has its electron in the n = 2 level. What is the minimum energy needed to ionise this atom?

Question 29

A sample of hydrogen gas has atoms excited to the n = 4 level. As they return to the ground state by every possible route, how many different wavelengths of light can be emitted?

Question 30

White light with a continuous spectrum passes through a cool sample of sodium vapour and then through a spectroscope. What is seen?

Question 31

Which of these sources gives a line emission spectrum?

Question 32

A mineral glows green when ultraviolet light shines on it. Why is the energy of each green photon less than the energy of each ultraviolet photon absorbed?

Question 33

In a laser, a photon passes an atom that is already in an excited state, causing stimulated emission. How does the emitted photon compare with the photon that caused it?

Question 34

For a laser to produce a strong beam, its medium must have a population inversion. What does this mean?

Question 35

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

The table gives energy levels of a hydrogen atom. A photon of energy 12.5 eV passes through hydrogen gas whose atoms are all in the ground state. What happens to the photon?

Question 36

The X-ray spectrum from a copper target has sharp peaks on top of a continuous background. How is each sharp peak produced?

Question 37

A strong characteristic line in the X-ray spectrum of copper has a photon energy of 8.05 keV. What is its wavelength? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 38

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

The table gives energy levels of a hydrogen atom. Hydrogen gas in a discharge tube emits a blue-green line of wavelength 486 nm. Which transition produces it? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 39

Mercury atoms in a fluorescent tube emit ultraviolet light of wavelength 254 nm. What is the energy of one of these photons in electronvolts? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 40

In the Standard Model, which gauge boson carries the electromagnetic force between charged particles?

Question 41

Which fundamental force is carried by the W and Z bosons?

Question 42

A sigma baryon is made of two up quarks and one strange quark. What is its charge, in units of e? Quark charges: up +⅔e, down −⅓e, strange −⅓e.

Question 43

A meson has a charge of −1e. Which quark and antiquark could it be made of? Quark charges: up +⅔e, down −⅓e, strange −⅓e. An antiquark has the opposite charge to its quark.

Question 44

A pion is a meson. What is its baryon number?

Question 45

Which of these particles is a lepton?

Question 46

Which of these proposed reactions breaks the conservation of lepton number? Leptons (such as e⁻, μ⁻ and neutrinos) have lepton number +1, their antiparticles −1, and every other particle 0.

Question 47

An electron and a positron, both almost at rest, annihilate and produce two photons of equal energy. What is the energy of each photon? Take mₑ = 9.11 × 10⁻³¹ kg and c = 3.00 × 10⁸ m s⁻¹.

Question 48

How does an antiproton compare with a proton?

Question 49

A proton and an antiproton, both almost at rest, annihilate. What is the total energy released? Take mₚ = 1.67 × 10⁻²⁷ kg and c = 3.00 × 10⁸ m s⁻¹.

Question 50

An electron and a positron at rest annihilate. Why must at least two photons be produced rather than one?

Question 51

Which set of quarks makes up a neutron? Quark charges: up +⅔e, down −⅓e, strange −⅓e.

Question 52

Ultraviolet light of wavelength 300 nm falls on a metal plate. The photoelectric current is just stopped by a stopping voltage of 1.20 V. What is the work function of the metal? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 53

Ultraviolet light of wavelength 250 nm falls on a copper plate whose work function is 4.70 eV. What is the maximum speed of the photoelectrons? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, 1 eV = 1.60 × 10⁻¹⁹ J and mₑ = 9.11 × 10⁻³¹ kg.

Question 54

A lambda baryon (up, down and strange quarks) decays into a proton (up, up, down) and a negative pion (a down quark and an anti-up antiquark). Quark charges: up +⅔e, down −⅓e, strange −⅓e. An antiquark has the opposite charge to its quark, and baryon number +⅓ for a quark, −⅓ for an antiquark. Which statement about this decay is correct?

Question 55

Light containing two wavelengths, 450 nm and 650 nm, falls at right angles on a grating with 500 lines per millimetre. What is the angle between the second-order maximum for 650 nm and the third-order maximum for 450 nm?

Question 56

A student shines a lamp's light through a coloured filter and then through two slits 0.300 mm apart. On a screen 2.50 m away, the distance from the centre of the first bright fringe to the centre of the eighth bright fringe in a row is 32.1 mm. Taking visible light to run from violet (400 nm) through blue, green (about 495 nm to 570 nm), yellow and orange to red (700 nm), what is the wavelength, and which colour is the light?

Question 57

A red laser of wavelength 650 nm shines at right angles onto a grating with 300 lines per millimetre. At what angle is the highest order that forms?

Question 58

Light of frequency 7.50 × 10¹⁴ Hz on a metal surface gives a stopping voltage of 1.05 V. The same surface is then lit with light of frequency 9.00 × 10¹⁴ Hz. What is the new stopping voltage? Take h = 6.63 × 10⁻³⁴ J s and e = 1.60 × 10⁻¹⁹ C.

Question 59

An X-ray tube accelerates electrons through 30.0 kV. What is the momentum of the shortest-wavelength X-ray photon it produces? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and e = 1.60 × 10⁻¹⁹ C.

Question 60

Electrons accelerated from rest through 600 V pass through a thin graphite film whose rows of atoms are 2.13 × 10⁻¹⁰ m apart. Treating the rows like a grating, d sin θ = mλ, at what angle is the first-order maximum? Take h = 6.63 × 10⁻³⁴ J s, e = 1.60 × 10⁻¹⁹ C and mₑ = 9.11 × 10⁻³¹ kg.

Question 61

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

The table gives energy levels of a hydrogen atom. Hydrogen atoms excited to n = 4 return to the ground state by every possible route. Visible light runs from 400 nm to 700 nm. How many of the emitted lines are visible? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 62

Energy levels of an atom in a gas discharge lamp, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−1.6
n = 3	−3.7
n = 2	−5.5
n = 1	−10.4

The table gives energy levels of the atoms in a gas discharge lamp. An atom in its ground state absorbs a photon that raises it to n = 4. It then returns to the ground state in two steps, first to n = 2 and then to n = 1. What is the wavelength of the photon emitted in the first step? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 63

Energy levels of a hydrogen atom, from n = 1 (the ground state) to n = 4.
Level	Energy (eV)
n = 4	−0.85
n = 3	−1.51
n = 2	−3.40
n = 1	−13.6

The table gives energy levels of a hydrogen atom. What is the longest wavelength of light that can ionise a hydrogen atom whose electron is in the n = 2 level? Take h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.

Question 64

An electron and a positron, each with kinetic energy 1.00 × 10⁻¹⁴ J, meet head-on at equal speeds and annihilate, producing two photons of equal energy. What is the wavelength of each photon? Take mₑ = 9.11 × 10⁻³¹ kg, h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹.

Question 65

A proposed decay turns a lambda baryon (up, down and strange quarks) into a positive pion (an up quark and an anti-down antiquark) and an electron. Quark charges: up +⅔e, down −⅓e, strange −⅓e. An antiquark has the opposite charge and baryon number to its quark; a quark has baryon number +⅓, and the electron has lepton number +1. Which conservation laws does this decay break?

Question 66

In the reaction p + p → p + K⁺ + X, the kaon K⁺ is an up quark with an anti-strange antiquark, and X is a particle that contains one strange quark. Quark charges: up +⅔e, down −⅓e, strange −⅓e. An antiquark has the opposite charge to its quark; a quark has baryon number +⅓ and an antiquark −⅓. Using conservation of charge and baryon number, which quarks make up X?