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 the family of transverse waves that all travel at 3.0 × 10⁸ m/s in a vacuum, from radio waves through visible light to gamma rays. These worked answers correct the 20 problems of the grade 8 science worksheet on electromagnetic spectrum, from order of the spectrum to sending letters in binary: each solution shows the formula, the substitution and the final answer with its unit.
Check your method against these model answers. Calculations show the formula, the substitution and the result in bold. For wave problems, convert the frequency to hertz before dividing, and for binary problems, write the place values above the digits.
Level: Grade 8 science (Year 9 · Class 8) · Curriculum: MS-PS4-3
Problem 1 Order of the spectrum
1. Radio, microwave, infrared, visible light, ultraviolet, X-ray, gamma.2. Radio waves have the longest wavelength: radio.
3. Gamma rays have the highest frequency and the most energy: gamma.
Problem 2 Speed of EM waves
1. The speed is 3.0 × 10⁸ m/s.2. No. EM waves can travel through a vacuum, so they do not need a material.
3. They have the same speed; neither is faster.
Problem 3 Match the use
1. Infrared.2. X-rays.
3. Microwaves (radio waves are also used in some links).
4. Gamma rays.
5. Ultraviolet.
Problem 4 Analogue or digital
1. Analogue, because the mercury can stop at any height.2. Digital, because it is stored as 1s and 0s.
3. Analogue, because brightness changes continuously.
4. Digital, because there are only two states.
Problem 5 Binary basics
1. The digits are 0 and 1.2. One byte is 8 bits.
3. 101 = 4 + 0 + 1 = 5.
Problem 6 Decimal to binary
1. 6 = 4 + 2, so 0110 (110).2. 9 = 8 + 1, so 1001.
3. 12 = 8 + 4, so 1100.
4. 15 = 8 + 4 + 2 + 1, so 1111.
Problem 7 AM radio wavelength
1. 900 kHz = 900 × 10³ Hz = 9.0 × 10⁵ Hz.2. λ = v ÷ f = 3.0 × 10⁸ ÷ 9.0 × 10⁵ = 333 m, which is 3.3 × 10² m.
3. They are radio waves.
Problem 8 Microwave oven
1. 2.45 GHz = 2.45 × 10⁹ Hz.2. λ = 3.0 × 10⁸ ÷ 2.45 × 10⁹ = 0.122 m, which is 12.2 cm.
Problem 9 Frequency of light
1. λ = 7.00 × 10⁻⁷ m, so f = 3.0 × 10⁸ ÷ 7.00 × 10⁻⁷ = 4.3 × 10¹⁴ Hz.2. λ = 4.00 × 10⁻⁷ m, so f = 3.0 × 10⁸ ÷ 4.00 × 10⁻⁷ = 7.5 × 10¹⁴ Hz.
3. Violet has the higher frequency because its wavelength is shorter.
Problem 10 Wavelengths in a table
1. 1 km: radio. 10 cm: microwave. 10 µm: infrared. 500 nm: visible light. 100 nm: ultraviolet. 1 nm: X-ray. 0.001 nm: gamma.2. The shortest wavelength has the highest frequency: gamma rays.
Problem 11 Sunburn on a cloudy day
1. Ultraviolet radiation.2. UV has a higher frequency than visible light, so its waves carry more energy and can damage the DNA in skin cells. It also passes through thin cloud.
3. Wear sunscreen, a hat or cover the skin: sunscreen or a hat.
Problem 12 Spot the errors
1. All EM waves travel at the same speed in a vacuum: 3.0 × 10⁸ m/s.2. A digital signal has only two levels, 0 and 1, and nothing between.
Problem 13 Binary to decimal
1. From the left the place values are 16, 8, 4, 2, 1.2. 16 + 0 + 4 + 2 + 0 = 22.
3. 16 + 8 + 0 + 0 + 1 = 25.
Problem 14 Reading a wave graph
1. Distance between crests = 5.0 − 1.0 = 4.0 m.2. f = v ÷ λ = 3.0 × 10⁸ ÷ 4.0 = 7.5 × 10⁷ Hz.
3. 7.5 × 10⁷ Hz = 75 MHz.
Problem 15 Rebuilding a digital signal
1. The pulses are high, high, low, high, low, low, high, low: 11010010.2. Each pulse is clearly above or below the threshold, so the receiver can decide 1 or 0 and rebuild a clean signal. The threshold removes the noise.
3. The noise would stay in the signal and be amplified with it.
Problem 16 Wi-Fi bands
1. At 2.4 GHz: λ = 3.0 × 10⁸ ÷ 2.4 × 10⁹ = 0.125 m. At 5.0 GHz: λ = 3.0 × 10⁸ ÷ 5.0 × 10⁹ = 0.060 m.2. 0.125 ÷ 0.060 = 2.1 times longer.
3. The higher frequency, 5.0 GHz, carries more energy.
Problem 17 Downloading a file
1. 15 MB × 8 = 120 Mbit.2. Time = 120 ÷ 20 = 6.0 s.
3. 2¹⁰ = 1024 values.
Problem 18 Satellite TV delay
1. 36 000 km = 3.6 × 10⁷ m, so up and down is 2 × 3.6 × 10⁷ = 7.2 × 10⁷ m.2. t = d ÷ v = 7.2 × 10⁷ ÷ 3.0 × 10⁸ = 0.24 s.
3. Microwaves (or radio waves).
Problem 19 Choosing the right wave
1. X-rays. They pass through soft tissue but are absorbed by bone, so bone shows on the image.2. Infrared. Warm objects give out more infrared, which a thermal camera detects in the dark.
3. X-rays are ionising and can damage cells, so repeated exposure raises the risk of harm. Staff limit their exposure.
Problem 20 Sending letters in binary
1. C = 3 = 00011, A = 1 = 00001, B = 2 = 00010. The message is 00011 00001 00010.2. 01000 = 8 = H and 00101 = 5 = E, so the message is HE.
3. Bits = 120 × 5 = 600, so time = 600 ÷ 2400 = 0.25 s.
