Senior 6 practice book · Unit 7 of 10

X-rays and Laser Radiations

50 questions that complete the Senior 6 quiz for this unit: 21 core and 29 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

The hot filament of an X-ray tube is what gives out the X-rays.The filament only releases electrons by thermionic emission; X-rays are produced at the target, where these fast electrons are suddenly slowed down or knock out inner electrons of the target atoms.
A patient keeps giving out X-rays, or becomes radioactive, after an X-ray photograph.X-rays are just electromagnetic waves: as soon as the tube is switched off there are none left, and they do not make the body radioactive.
A laser makes light stronger because its mirrors reflect it many times.The mirrors only send photons back through the medium; the light is amplified by stimulated emission, which only wins over absorption when there is a population inversion.
Laser light is dangerous because each laser photon carries a huge amount of energy.A visible laser photon has an ordinary energy of about 2 eV, much less than an X-ray photon; the danger comes from the narrow beam being focused by the eye onto a tiny spot, giving a very high intensity.
Laser light is coherent because all the atoms emit their photons spontaneously at the same moment.Spontaneous emission is random in time and direction; coherence comes from stimulated emission, in which each new photon copies the phase, direction and frequency of the photon that triggered it.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Production of X-rays: the X-ray tube (thermionic emission, accelerating voltage, target, vacuum, cooling)
Properties of X-rays, their hazards and safety in the X-ray room
The X-ray spectrum: continuous (braking) radiation, characteristic lines and the cut-off wavelength λ_min = hc/(eV)
Controlling intensity and quality: tube current, tube voltage, hard and soft X-rays, filters
Energy calculations for the X-ray tube: electron energy and speed, power, efficiency and heat in the target
Attenuation of X-rays: half-value thickness, I = I₀e^−μx, effect of atomic number, contrast media
X-ray diffraction by crystals and Bragg's law 2d sin θ = nλ
Uses of X-rays in medicine, industry and research (radiography, CT, flaw detection)
Energy levels, absorption, spontaneous and stimulated emission of photons
Population inversion, pumping, metastable states, three-level and four-level systems
Construction of a laser and types of laser (optical cavity, ruby, helium–neon, CO₂, semiconductor diode)
Properties of laser light compared with ordinary light: monochromatic, coherent, collimated, intense
Laser calculations: photon energy, photon rate, power, pulse power and intensity
Everyday and industrial uses of lasers (optical discs, cutting, surveying, rangefinding, holography)

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 29 harder ones are marked ★ Challenge.

1True or false
The filament (cathode) of an X-ray tube is connected to the positive terminal of the high-voltage supply.
Show answer
Answer: False
The filament is the cathode and is at a negative potential; the target is the positive anode, so the electrons are pulled from the filament to the target.
Common mistakeLearners often think the hot part must be positive; electrons are negative and move towards the positive anode, so the filament must be negative.
2True or false · ★ Challenge
Two half-value thicknesses of lead stop an X-ray beam completely.
Show answer
Answer: False
Each half-value thickness halves the intensity, so after two a quarter (25 %) of the beam still passes.
Common mistakeAdding "half + half = all" treats attenuation as a fixed amount removed per layer; each layer removes half of what is LEFT.
3True or false · ★ Challenge
A filtered lamp that lets through only one narrow band of red light gives light that is coherent, just like laser light.
Show answer
Answer: False
A filter makes the light nearly monochromatic, but the atoms of the lamp still emit at random times, so the phases remain random; only stimulated emission gives coherent light.
Common mistakeLearners often think "one colour" means "coherent"; monochromatic and coherent are two different properties.
4True or false
In a semiconductor diode laser, the light is produced when electrons and holes recombine at a p–n junction.
Show answer
Answer: True
A forward current drives electrons and holes into the junction; when they recombine they emit photons, and the polished ends of the crystal act as the mirrors.
Common mistakeLearners sometimes think all lasers need a gas tube; in a diode laser the active medium is a semiconductor junction.
5True or false · ★ Challenge
Doubling the tube current at a fixed voltage doubles the intensity of the X-ray beam but leaves the cut-off wavelength and the positions of the line peaks unchanged.
Show answer
Answer: True
Twice as many electrons per second give twice as many photons, but each electron still has energy eV, so the shape of the spectrum is the same.
Common mistakeLearners often expect the cut-off to move with current; only the voltage changes λ_min.
6True or false
Lasers can cut metal sheets because the focused beam has such a high intensity that it melts or vaporises the metal along a very narrow line.
Show answer
Answer: True
Focusing a beam of hundreds of watts onto a spot a fraction of a millimetre wide gives an enormous intensity.
Common mistakeLearners sometimes think the laser "pushes" the metal apart; the cut is made by heating, not by force.
7Fill in the blank · ★ Challenge
For a standing wave to build up in a laser cavity of length L, a whole number of ______ wavelengths must fit into L.
Show answer
Answer: half
The mirrors are nodes, so L = nλ/2, as for a string fixed at both ends.
Common mistakeAnswering "whole" wavelengths misses half of the allowed modes; the condition is L = nλ/2.
8Fill in the blank · ★ Challenge
A tube with a tungsten target is replaced by one with a molybdenum target at the same voltage. The cut-off wavelength stays the same, but the ______ lines move to new wavelengths.
Show answer
Answer: characteristic
Characteristic lines come from electrons falling between inner shells of the target atoms, so they are a "fingerprint" of the target metal.
Common mistakeSaying the cut-off also moves is wrong; it depends only on the tube voltage.
9True or false
An atom can absorb a photon and jump between two energy levels only if the photon's energy equals the energy difference between those levels.
Show answer
Answer: True
Energy levels are fixed, so only photons with hf = E₂ − E₁ can be absorbed in such a jump; other photons pass by.
Common mistakeLearners think an atom can take any part of a photon's energy; in a jump between levels the whole photon is absorbed and its energy must match.
10Fill in the blank · ★ Challenge
In Bragg's law 2d sin θ = nλ, the angle θ is measured between the X-ray beam and the crystal ______, not the normal.
Show answer
Answer: planes (atomic planes)
θ is the glancing angle between the beam and the layers of atoms; the total deviation of the beam is 2θ.
Common mistakeUsing the angle from the normal, as in optics, gives sin of the wrong angle and a wrong spacing.
11Fill in the blank
In a helium–neon laser the gas is pumped by an electric ______ passing through it, while a ruby laser is pumped by a flash lamp.
Show answer
Answer: discharge (current)
Electrons in the discharge collide with helium atoms and excite them; helium then passes the energy to neon atoms.
Common mistakeAnswering "magnet" or "heater" is wrong: pumping must lift atoms to particular excited levels, which collisions with electrons in a discharge can do.
12Fill in the blank · ★ Challenge
For a beam with linear attenuation coefficient μ, the half-value thickness is x½ = ______ ÷ μ.
Show answer
Answer: ln 2 (0.693)
Setting I = I₀/2 in I = I₀e^−μx gives e^−μx½ = 1/2, so μx½ = ln 2.
Common mistakeWriting x½ = 2 ÷ μ forgets that the intensity falls exponentially, so the logarithm ln 2 appears, not 2.
13Fill in the blank
A three-dimensional image recorded using the interference of laser light, as seen on bank cards and banknotes, is called a ______.
Show answer
Answer: hologram
Holography needs coherent light, so that the reference beam and the light from the object form a stable interference pattern.
Common mistakeAnswering "photograph" misses the point: a photograph records only brightness, while a hologram also records the phase of the light.
14Multiple choice · ★ Challenge
Why can shining light on a simple two-level system never give a lasting population inversion?
1. ALight can never raise atoms from a lower energy level to a higher one
2. BThe pump light ionises all the atoms in the medium
3. CThe two levels would give out photons of different wavelengths
4. DPump light also stimulates emission, so levels at best fill equally
Show answer
Answer: D. Pump light also stimulates emission, so levels at best fill equally
The same photons that lift atoms up also stimulate excited atoms to come down, so the populations can only approach equality; a third (and fourth) level is needed.
Common mistakeChoosing "light cannot raise atoms" contradicts absorption itself; the problem is that absorption and stimulated emission are equally likely.
15Fill in the blank · ★ Challenge
An X-ray tube changes 0.80 % of its electrical input into X-rays. If the X-ray output power is 12 W, the electrical input power is ______ W.
Show answer
Answer: 1500
Input = output ÷ efficiency = 12 ÷ 0.0080 = 1500 W.
Common mistakeMultiplying 12 by 0.80 (giving 9.6 W) uses the efficiency the wrong way round: the input must be much larger than the output.
16Multiple choice
A DVD player reads the data on a disc with a laser because:
1. AIts light is hot enough to melt the pits into sound
2. BIts beam can be focused onto the tiny pits on the disc
3. CIts light passes straight through the plastic disc
4. DIts beam magnetises small regions of the disc's metal surface
Show answer
Answer: B. Its beam can be focused onto the tiny pits on the disc
The narrow, monochromatic beam focuses to a spot about 1 μm across; the reflected light changes between pits and flat parts, giving the 0s and 1s.
Common mistakeChoosing "magnetises small regions" mixes up optical discs with magnetic hard drives; a DVD is read by reflected light.
17Short answer · ★ Challenge
A radiographer at a district hospital stands behind a lead-lined screen during each exposure, keeps as far from the tube as the room allows and wears a dosimeter badge. Give the reason for each of these three measures.
Show answer
Model answer: Lead is dense and has a high atomic number, so it absorbs X-rays strongly, including those scattered from the patient. Intensity falls quickly with distance from the tube and the patient, so standing far away lowers the dose. The badge records the total dose received over time so that it can be checked against the safe limit; it does not give protection.
Common mistakeA common error is to think the dosimeter badge protects the worker; it only measures the dose.
18Multiple choice
Which observation shows that X-rays carry no electric charge?
1. AThey make some materials glow with visible light
2. BThey blacken photographic film after developing
3. CThey ionise the air and other gases they pass through
4. DThey are not deflected by electric or magnetic fields
Show answer
Answer: D. They are not deflected by electric or magnetic fields
A charged beam would be bent by electric and magnetic fields; X-rays (photons) go straight on, so they are uncharged.
Common mistakeChoosing "they ionise the air" is tempting, but uncharged photons can also ionise atoms by giving their energy to electrons; ionising does not need a charge.
19Multiple choice · ★ Challenge
Blu-ray discs are read with blue-violet lasers (405 nm) instead of the red lasers (650 nm) of DVDs. Why can a Blu-ray disc hold much more data?
1. ABlue photons travel faster, so data is read more quickly
2. BBlue light has a longer wavelength, so it reflects better from the disc
3. CA shorter wavelength focuses to a smaller spot, so pits can be smaller
4. DRed light slowly damages the plastic of the disc surface
Show answer
Answer: C. A shorter wavelength focuses to a smaller spot, so pits can be smaller
The smallest spot a beam can be focused to is about one wavelength across; a shorter wavelength allows smaller pits packed closer together.
Common mistakeChoosing "blue photons travel faster" is wrong: all light travels at the same speed in a vacuum; the advantage is the shorter wavelength.
20Fill in the blank
When X-rays fall on certain materials, such as zinc sulfide, the material gives out visible light. This effect, used in X-ray screens, is called ______.
Show answer
Answer: fluorescence
The X-ray energy excites the atoms of the screen, which then emit visible light that can be seen or recorded.
Common mistakeAnswering "reflection" is wrong: the screen does not send the X-rays back; it changes their energy into visible light.
21Multiple choice · ★ Challenge
A laser beam leaves a building in Kigali with a diameter of 2.0 mm and spreads with a total angle of 0.50 milliradian. About how wide is the beam 1.0 km away?
1. A0.25 m
2. B5.0 m
3. C2.0 mm
4. D0.50 m
Show answer
Answer: D. 0.50 m
Extra width ≈ distance × angle = 1000 × 0.50 × 10⁻³ = 0.50 m; adding the 2.0 mm start width gives about 0.50 m.
Common mistakeChoosing 0.25 m uses only half of the angle; 0.50 mrad is already the TOTAL spread, so the width grows by L × θ = 0.50 m.
22Multiple choice · ★ Challenge
The linear attenuation coefficient of bone for a certain X-ray beam is 0.50 cm⁻¹. What fraction of the beam passes through 3.0 cm of bone?
1. A0.78
2. B0.61
3. C0.25
4. D0.22
Show answer
Answer: D. 0.22
I/I₀ = e^−μx = e^{−0.50 × 3.0} = e^−1.5 = 0.22.
Common mistakeChoosing 0.78 gives the fraction ABSORBED (1 − 0.22), not the fraction that passes through.
23Multiple choice
In a four-level laser, the lasing transition ends on a level that:
1. AEmpties very quickly, so it stays almost empty
2. BIs the ground state, where most of the atoms are
3. CIs metastable, so atoms stay in it a long time
4. DIs higher in energy than the upper lasing level
Show answer
Answer: A. Empties very quickly, so it stays almost empty
Atoms leave the lower lasing level very fast, so even a small number of atoms in the upper level gives a population inversion.
Common mistakeChoosing "metastable" confuses the two lasing levels: it is the UPPER lasing level that must be metastable.
24Fill in the blank · ★ Challenge
A laser emits 3.0 × 10¹⁶ photons per second, each of energy 3.3 × 10⁻¹⁹ J. Its output power is ______ mW.
Show answer
Answer: 9.9
P = number per second × energy per photon = 3.0 × 10¹⁶ × 3.3 × 10⁻¹⁹ = 9.9 × 10⁻³ W = 9.9 mW.
Common mistakeDividing the two numbers instead of multiplying gives a meaningless answer; power is energy per second, so multiply.
25Short answer · ★ Challenge
Before an X-ray of the stomach, a patient swallows a "barium meal" (barium sulfate). Explain why this makes the stomach show clearly on the image.
Show answer
Model answer: Soft tissues of the stomach absorb X-rays about as much as the tissue around them, so they give little contrast. Barium has a high atomic number, and absorption rises steeply with atomic number, so the barium-filled stomach absorbs X-rays strongly and shows white against the darker surrounding tissue.
Common mistakeA common error is to think barium gives out X-rays or is radioactive; it simply absorbs X-rays strongly.
26Multiple choice
The half-value thickness of a material for an X-ray beam is the thickness that:
1. AAbsorbs every photon below half the maximum energy
2. BReduces the intensity of the beam to half
3. CHalves the wavelength of the X-rays passing through
4. DIs half as thick as needed to stop the beam completely
Show answer
Answer: B. Reduces the intensity of the beam to half
After one half-value thickness the intensity is I₀/2, after two I₀/4, and so on.
Common mistakeChoosing "half as thick as needed to stop the beam" assumes absorption is linear; the intensity falls exponentially and never reaches exactly zero.
27Short answer · ★ Challenge
A thin aluminium filter is often placed over the window of a medical X-ray tube. Explain how this lowers the patient's dose without spoiling the image.
Show answer
Model answer: Soft (low-energy, long-wavelength) X-rays are absorbed in the first few centimetres of the patient's skin and tissue, so they add to the dose but never reach the detector to form the image. Aluminium absorbs these soft X-rays but lets most of the hard X-rays through, so the beam that reaches the patient is the useful, penetrating part.
Common mistakeA common error is to think a filter makes the X-rays "weaker for safety" in general; it removes mainly the soft X-rays that would only harm the skin.
28Multiple choice
Which type of laser is found in laser pointers, DVD players and fibre-optic transmitters?
1. ACarbon dioxide (CO₂) gas laser
2. BRuby crystal laser
3. CSemiconductor diode laser
4. DHelium–neon gas laser
Show answer
Answer: C. Semiconductor diode laser
Diode lasers are tiny, cheap, efficient and run from a small battery, so they suit small devices.
Common mistakeChoosing helium–neon is tempting because it is the classic school red laser, but it needs a glass tube and a high-voltage supply, too big for a pointer.
29Short answer · ★ Challenge
Explain why light passing through an ordinary gas at room temperature is absorbed more than it is amplified, even though stimulated emission can happen.
Show answer
Model answer: At room temperature nearly all the atoms are in the ground state and very few are excited. A passing photon is therefore far more likely to meet a ground-state atom and be absorbed than an excited atom and cause stimulated emission. Amplification only wins when there are more atoms in the upper level than in the lower one (population inversion).
Common mistakeA common error is to think stimulated emission happens by itself whenever light passes; it needs excited atoms, which are rare without pumping.
30Multiple choice
X-rays, rather than visible light, are used to study how atoms are arranged in crystals because:
1. AThey are reflected only by the nuclei of the atoms
2. BTheir wavelengths are similar to the spacing of the atoms
3. CThey travel more slowly inside crystals than light
4. DCrystals give out X-rays of their own when they are heated strongly
Show answer
Answer: B. Their wavelengths are similar to the spacing of the atoms
Diffraction is strong when the wavelength is about the same size as the spacing of the "grating"; atomic spacings are about 0.1–0.3 nm, like X-ray wavelengths.
Common mistakeChoosing "reflected by nuclei" is wrong: X-rays are scattered mainly by the electrons of the atoms, and the pattern comes from interference.
31Short answer · ★ Challenge
In many hospital X-ray tubes the tungsten anode is a disc that spins quickly during an exposure. Explain the purpose of the spinning anode and give one other feature of the tube that removes heat from the target.
Show answer
Model answer: The electron beam always hits the same spot in space, but as the disc spins, a different part of the disc is under the beam, so the heat is spread round a ring instead of one small spot; this stops the tungsten melting or pitting. Other features: the anode is mounted on copper (a good thermal conductor), and the tube sits in oil that carries heat away to cooling fins or a fan.
Common mistakeA common error is to think that the spinning changes the energy of the X-rays; it only spreads the heat, because about 99 % of the electron energy becomes heat.
32Multiple choice
A radiographer changes from imaging a child's hand to imaging an adult's thick thigh bone. What should she do?
1. ARaise the filament current to give each photon more energy
2. BLower the tube voltage so fewer X-rays are absorbed in the leg
3. CRaise the tube voltage to give harder, more penetrating X-rays
4. DChange to a target metal with a lower melting point
Show answer
Answer: C. Raise the tube voltage to give harder, more penetrating X-rays
The tube voltage sets the maximum photon energy; harder (higher-energy) X-rays get through thick tissue and bone.
Common mistakeChoosing "raise the filament current" is the classic error: more current gives more photons, not more energetic photons.
33Multiple choice · ★ Challenge
A research laboratory uses cobalt X-rays of wavelength 0.180 nm on a crystal whose atomic planes are 0.315 nm apart. At what glancing angle θ is the first-order Bragg maximum? (2d sin θ = nλ)
1. A16.6°
2. B34.8°
3. C73.4°
4. D8.3°
Show answer
Answer: A. 16.6°
sin θ = nλ/(2d) = 0.180 ÷ (2 × 0.315) = 0.286, so θ = 16.6°.
Common mistakeChoosing 34.8° comes from leaving out the 2 in 2d sin θ; choosing 73.4° measures θ from the normal instead of from the planes.
34Multiple choice · ★ Challenge
A dental laser fires 20 pulses each second. Each pulse carries 0.15 J and lasts 0.10 ms. What are the average power and the peak power during a pulse?
1. A3.0 W; 1.5 kW
2. B0.0075 W; 1.5 kW
3. C3.0 W; 15 W
4. D3.0 W; 30 kW
Show answer
Answer: A. 3.0 W; 1.5 kW
Average power = 20 × 0.15 = 3.0 W. Peak power = energy ÷ pulse time = 0.15 ÷ 1.0 × 10⁻⁴ = 1500 W = 1.5 kW.
Common mistakeChoosing 0.0075 W divides the pulse energy by the number of pulses; the energy per second is the energy per pulse TIMES the number of pulses per second.
35Multiple choice
In a laser, the active medium sits between two mirrors that form an optical cavity. The main job of the cavity is to:
1. AKeep the medium cool while it is being pumped hard
2. BSend photons through the medium many times
3. CTurn the light into one single colour
4. DStore the pump energy until the beam is needed
Show answer
Answer: B. Send photons through the medium many times
Each pass through the inverted medium adds more stimulated photons, so the beam builds up; the partly transmitting mirror lets some out.
Common mistakeChoosing "turn the light into one colour" gives the cavity the job of the medium: the single wavelength comes from the energy gap of the lasing transition.
36Multiple choice · ★ Challenge
In tungsten, the K shell has energy −69.5 keV and the L shell −10.2 keV. An electron falls from the L shell into a gap in the K shell. What is the wavelength of the X-ray emitted? (hc = 1.99 × 10⁻²⁵ J m, 1 eV = 1.6 × 10⁻¹⁹ J)
1. A0.018 nm
2. B0.021 nm
3. C0.016 nm
4. D0.12 nm
Show answer
Answer: B. 0.021 nm
ΔE = 69.5 − 10.2 = 59.3 keV = 9.49 × 10⁻¹⁵ J; λ = hc/ΔE = 1.99 × 10⁻²⁵ ÷ 9.49 × 10⁻¹⁵ = 2.1 × 10⁻¹¹ m = 0.021 nm.
Common mistakeChoosing 0.018 nm comes from using the K-shell energy 69.5 keV alone; the photon carries only the DIFFERENCE between the two levels.
37Multiple choice
An engineer X-rays a weld in a new steel water pipe to look for hidden cracks. On the developed film, a crack shows as:
1. AA lighter line, as the crack absorbs more X-rays
2. BA bright glow, as the crack gives out its own light
3. CA darker line, as more X-rays pass through the gap
4. DNothing, as X-rays cannot pass through any steel
Show answer
Answer: C. A darker line, as more X-rays pass through the gap
Where there is a crack there is less steel to absorb the X-rays, so more reach the film and it is darker there.
Common mistakeChoosing "lighter line" reverses the film rule: on film, places where MORE X-rays arrive turn darker, as with soft tissue next to bone.
38Multiple choice · ★ Challenge
An atom has energy levels at 0 (ground state), 1.8 eV and 3.0 eV. Atoms in the 3.0 eV level can fall to either lower level. Which transition gives the longest wavelength, and what is it? (h = 6.63 × 10⁻³⁴ J s, c = 3.0 × 10⁸ m/s, 1 eV = 1.6 × 10⁻¹⁹ J)
1. A1.8 eV → 0, 691 nm
2. B3.0 eV → 0, 414 nm
3. C3.0 eV → 1.8 eV, 1.04 nm
4. D3.0 eV → 1.8 eV, 1040 nm
Show answer
Answer: D. 3.0 eV → 1.8 eV, 1040 nm
The smallest energy gap gives the longest wavelength: ΔE = 1.2 eV = 1.92 × 10⁻¹⁹ J, λ = hc/ΔE = 1.99 × 10⁻²⁵ ÷ 1.92 × 10⁻¹⁹ = 1.04 × 10⁻⁶ m = 1040 nm.
Common mistakeChoosing 3.0 eV → 0 picks the biggest jump, which gives the SHORTEST wavelength, because λ = hc/ΔE.
39Multiple choice · ★ Challenge
A graph of X-ray intensity against wavelength from a tube begins at a cut-off wavelength λ_min. A student says this cut-off depends on the metal used for the target. Which evaluation is correct?
1. AYes: atoms of higher atomic number give a smaller λ_min
2. BYes: λ_min is the wavelength of the tallest line peak
3. CNo: λ_min = hc/(eV) depends only on the tube voltage
4. DNo: λ_min depends only on the tube current used
Show answer
Answer: C. No: λ_min = hc/(eV) depends only on the tube voltage
The shortest wavelength comes from an electron giving all its energy eV to one photon, so hc/λ_min = eV; the target metal does not appear in this equation.
Common mistakeChoosing "higher atomic number" mixes up the cut-off with the characteristic lines: it is the line wavelengths that depend on the target metal.
40Multiple choice
Why is the inside of an X-ray tube kept as a vacuum?
1. ASo electrons reach the target without hitting gas
2. BSo the X-rays travel faster than in air
3. CSo the filament does not have to be heated by a current
4. DSo the metal target cannot become radioactive in use
Show answer
Answer: A. So electrons reach the target without hitting gas
Gas molecules would scatter and slow the electrons (and ionise), so they would not hit the target with the full energy eV.
Common mistakeChoosing "X-rays travel faster" confuses the electrons with the X-rays; X-rays travel at almost the same speed in air as in a vacuum.
41Multiple choice · ★ Challenge
A dental X-ray tube runs at 65 kV with a current of 7.0 mA for an exposure of 0.20 s. How much electrical energy is supplied during one exposure?
1. A91 J
2. B455 J
3. C0.091 J
4. D9.1 × 10⁴ J
Show answer
Answer: A. 91 J
E = VIt = 65 000 × 0.0070 × 0.20 = 91 J.
Common mistakeChoosing 9.1 × 10⁴ J comes from leaving the current as 7.0 instead of 0.0070 A; 455 J is the power VI in watts, not multiplied by the time.
42Short answer
Give two advantages of a CT scan over an ordinary X-ray photograph and one disadvantage.
Show answer
Model answer: Advantages (any two): it gives cross-sectional slices and 3D images, so organs do not overlap; it shows soft tissues of similar density that a plain X-ray cannot separate; the exact position and size of a tumour can be measured. Disadvantage: the patient receives a much larger dose of ionising radiation (it is also more expensive and slower).
Common mistakeA common error is to say CT uses no ionising radiation (that is MRI); CT uses X-rays from many directions, so its dose is higher.
43Short answer · ★ Challenge
A crystal used in an X-ray spectrometer has atomic planes 0.20 nm apart. Find the longest wavelength it can diffract in first order, and explain why it cannot diffract visible light.
Show answer
Model answer: sin θ cannot be more than 1, so the largest λ in first order is 2d sin 90° = 2 × 0.20 = 0.40 nm. Visible light has wavelengths of about 400–700 nm, more than 1000 times 2d, so no angle satisfies Bragg's law and there are no diffracted beams.
Common mistakeLearners often think any wave can be diffracted at some angle; Bragg's law needs nλ ≤ 2d, so long waves give no maxima at all.
44Short answer · ★ Challenge
A CO₂ laser (wavelength 10.6 μm) cuts steel sheet in a Kigali metal workshop, while a helium–neon laser (633 nm) is used only to line up the parts. Compare the photon energies of the two lasers and explain why the CO₂ laser can still cut metal.
Show answer
Model answer: Photon energy E = hc/λ, so E is inversely proportional to λ: the He–Ne photon carries 10 600 ÷ 633 ≈ 17 times more energy (3.1 × 10⁻¹⁹ J against 1.9 × 10⁻²⁰ J). Cutting is a heating effect that depends on the POWER delivered, not the energy of one photon; a CO₂ laser gives hundreds or thousands of watts, focused to a tiny spot, so the intensity melts the steel, while a He–Ne laser gives only a few milliwatts.
Common mistakeA common error is to think the laser with the more energetic photons must be the more powerful one; power = number of photons per second × energy per photon.
45Short answer
Explain why the continuous X-ray spectrum has a sharp minimum wavelength but no sharp maximum wavelength.
Show answer
Model answer: An electron cannot give a photon more than its whole kinetic energy eV, so there is a largest photon energy and therefore a smallest wavelength hc/(eV). Electrons can lose any small part of their energy in each collision, so very low-energy (long-wavelength) photons are possible; their intensity just fades because they are absorbed in the target and the glass window.
Common mistakeLearners often think there is also a fixed longest wavelength; small energy losses can be as small as you like, so there is no sharp long-wavelength limit.
46Short answer · ★ Challenge
A tungsten anode of mass 0.20 kg (specific heat capacity 134 J kg⁻¹ K⁻¹) is hit by a 100 kV, 10 mA electron beam for 0.40 s; 99 % of the energy becomes heat. Calculate the temperature rise of the anode if no heat escapes.
Show answer
Model answer: Energy supplied = VIt = 100 000 × 0.010 × 0.40 = 400 J; heat = 0.99 × 400 = 396 J. ΔT = Q/(mc) = 396 ÷ (0.20 × 134) ≈ 15 K (about 15 °C) for each exposure.
Common mistakeA common slip is to forget to change 100 kV and 10 mA into volts and amperes, which gives an energy a million times too big or too small.
47Short answer
Compare the light from a filament lamp with the light from a laser under three headings: range of wavelengths, phase of the waves and direction of travel.
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Model answer: Wavelengths: the lamp gives a continuous range of many wavelengths; the laser gives a single, very narrow wavelength (monochromatic). Phase: the lamp's waves have random phases (incoherent); the laser's waves are in step (coherent). Direction: the lamp sends light in all directions; the laser gives a narrow, almost parallel beam (collimated).
Common mistakeA common error is to describe the laser as "brighter" only; brightness comes from the three properties together, which a lamp does not have.
48Short answer · ★ Challenge
A learner measures the X-ray count rate behind copper sheets. Thickness (mm): 0, 0.5, 1.0, 1.5, 2.0. Count rate (per s): 800, 566, 400, 283, 200. Find the half-value thickness and the linear attenuation coefficient, and predict the count rate behind 3.0 mm.
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Model answer: The count rate halves from 800 to 400 in 1.0 mm (and 400 to 200 in the next 1.0 mm), so x½ = 1.0 mm. μ = ln 2/x½ = 0.693 ÷ 1.0 = 0.69 mm⁻¹ (693 m⁻¹). 3.0 mm is three half-value thicknesses: 800 ÷ 2³ = 100 per s.
Common mistakeA common error is to read the drop 800 → 566 in 0.5 mm as a straight-line fall and predict zero at about 2.7 mm; the fall is exponential.
49Short answer
Surveyors on a new road from Kigali to Musanze use a laser rangefinder. A laser pulse returns from a reflector 4.0 μs after it is sent. Calculate the distance to the reflector and give one reason why a laser is used.
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Model answer: Distance = (speed × time) ÷ 2 = (3.0 × 10⁸ × 4.0 × 10⁻⁶) ÷ 2 = 600 m. A laser is used because its narrow, parallel beam hits only the reflector and stays strong over long distances, so the returning pulse can be detected and timed.
Common mistakeForgetting to divide by 2 gives 1200 m; the pulse travels to the reflector AND back.
50Short answer · ★ Challenge
A 2.0 mW laser beam enters the eye and is focused by the lens to a spot of diameter 20 μm on the retina. Calculate the intensity on the retina and compare it with the intensity of bright sunlight (about 1000 W/m²).
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Model answer: Area = πr² = π × (10 × 10⁻⁶)² = 3.1 × 10⁻¹⁰ m². Intensity = P/A = 2.0 × 10⁻³ ÷ 3.1 × 10⁻¹⁰ ≈ 6.4 × 10⁶ W/m², about 6400 times bright sunlight, enough to burn the retina.
Common mistakeA common slip is to use the diameter (20 μm) as the radius, which makes the area four times too big and the intensity four times too small.