The problems are on the electromagnetic spectrum worksheet. Try them on your own first, then compare with the answers below.
Quick answer: The electromagnetic spectrum is a family of transverse waves that travel at 3.0 × 10⁸ m/s in a vacuum. These worked answers correct the 20 problems of the Physics 9-10 worksheet on electromagnetic spectrum, from order of the spectrum to two radio waves: each solution shows the formula, the substitution and the final answer with its unit.
Complete answers follow each problem in the same order. Check that you converted prefixes before using the wave equation, and that radar and echo problems use only half of the total distance.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: HS-PS4-4, HS-PS4-5
Problem 1 Order of the spectrum
Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.Problem 2 Shared properties
1. 3.0 × 10⁸ m/s.2. Transverse.
3. No, they can travel through a vacuum, which is how sunlight reaches Earth.
Problem 3 Match the use
1. Infrared.2. Gamma rays.
3. X-rays.
4. Microwaves (or radio waves).
5. Visible light.
6. Ultraviolet.
Problem 4 FM radio wavelength
1. 91.5 MHz = 91.5 × 10⁶ Hz = 9.15 × 10⁷ Hz.2. λ = c ÷ f = 3.0 × 10⁸ ÷ 9.15 × 10⁷ = 3.3 m.
Problem 5 Unit conversions
1. 2.4 GHz = 2.4 × 10⁹ Hz.2. 550 nm = 550 × 10⁻⁹ m = 5.5 × 10⁻⁷ m.
3. 0.12 nm = 0.12 × 10⁻⁹ m = 1.2 × 10⁻¹⁰ m.
Problem 6 Name the regions
1. Microwaves, ultraviolet, gamma rays.2. The right-hand end (gamma rays).
3. The second ? (ultraviolet) borders the X-ray region on its right.
Problem 7 Colour of a sodium lamp
1. 590 nm = 5.90 × 10⁻⁷ m.2. f = c ÷ λ = 3.0 × 10⁸ ÷ 5.90 × 10⁻⁷ = 5.1 × 10¹⁴ Hz.
Problem 8 Mobile network bands
1. At 1.8 GHz: λ = 3.0 × 10⁸ ÷ 1.8 × 10⁹ = 0.17 m. At 3.5 GHz: λ = 3.0 × 10⁸ ÷ 3.5 × 10⁹ = 0.086 m.2. The 3.5 GHz wave is shorter; the ratio is 0.167 ÷ 0.0857 = 1.9 times.
Problem 9 Radar echo from the Moon
1. Distance = speed × time = 3.0 × 10⁸ × 2.56 = 7.68 × 10⁸ m.2. This is there and back, so the Moon is 3.84 × 10⁸ m away.
Problem 10 Holes in the microwave door
1. 12 cm = 120 mm.2. The holes are much smaller than the 120 mm wavelength, so microwaves cannot pass through. Light has a wavelength far smaller than the hole, so it passes through freely.
Problem 11 Waves and frequencies
A: λ = 3.0 m, radio. B: λ = 3.0 × 10⁻⁴ m (0.30 mm), infrared. C: λ = 3.0 × 10⁻⁸ m (30 nm), ultraviolet. D: λ = 1.0 × 10⁻¹⁰ m (0.10 nm), X-ray.Problem 12 Sunburn at midday
1. Ultraviolet radiation.2. UV photons carry enough energy to damage molecules such as DNA in skin cells, so cells die or mutate.
3. Use sunscreen, wear a hat and long sleeves, and avoid the midday Sun.
Problem 13 Ionising or not
1. X-rays are ionising.2. Microwaves have a much lower frequency, so each wave carries too little energy to remove an electron from an atom; they can only heat tissue.
Problem 14 Vet checks cattle
1. All objects emit infrared, and hotter objects emit more, so the camera records more signal from a feverish animal.2. A normal camera needs visible light, and a dark shed gives none.
Problem 15 Spot the errors
1. All EM waves travel at the same speed, 3.0 × 10⁸ m/s, in a vacuum.2. Gamma rays have the shortest wavelength; radio waves are the longest.
3. Cooking is heating, not ionising; microwaves are non-ionising.
Problem 16 Antenna length
1. λ = 3.0 × 10⁸ ÷ 9.00 × 10⁸ = 0.333 m.2. L = λ ÷ 4 = 0.0833 m = 8.3 cm.
3. The frequency doubles, so the wavelength halves; the antenna is 4.2 cm.
Problem 17 Light from the Sun
1. t = d ÷ c = 1.50 × 10¹¹ ÷ 3.00 × 10⁸ = 500 s.2. 500 s = 8 min 20 s.
3. X-rays travel at the speed of light; charged particles are slower than light, so they arrive later.
Problem 18 Chest X-ray and background
1. 2.4 ÷ 365 = 0.0066 mSv per day.2. 0.020 ÷ 0.00658 = 3.0 days.
3. X-rays are ionising; the risk of damage adds up with every dose, so doctors only use them when the benefit is greater than the risk.
Problem 19 Sterilising with gamma rays
1. Gamma rays ionise molecules in the bacteria, damaging DNA so they cannot survive or reproduce.2. Gamma rays penetrate the packaging, so the gloves stay sterile; there is no need to heat them.
3. Operate the source in a thick concrete or lead-lined room, with the workers outside.
Problem 20 Two radio waves
1. A: 8.0 ÷ 2 = 4.0 m. B: 8.0 ÷ 8 = 1.0 m.2. A: f = 3.0 × 10⁸ ÷ 4.0 = 7.5 × 10⁷ Hz. B: f = 3.0 × 10⁸ ÷ 1.0 = 3.0 × 10⁸ Hz.
3. Wave A, because the longer the wavelength, the more it diffracts around obstacles.
