Q1: Electromagnetic radiation having a 15.0-μm wavelength is classified as infrared radiation. What is its frequency? Given that the speed of light is 3 × 10⁸ m/s.
Given:
Wavelength, λ = 15.0 μm = 15.0 × 10⁻⁶ m
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
f = c / λ
Calculation:
f = (3 × 10⁸) / (15.0 × 10⁻⁶)
f = (3 × 10⁸) / (1.5 × 10⁻⁵)
f = 2 × 10¹³ Hz
Answer: 2 × 10¹³ Hz
Wavelength, λ = 15.0 μm = 15.0 × 10⁻⁶ m
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
f = c / λ
Calculation:
f = (3 × 10⁸) / (15.0 × 10⁻⁶)
f = (3 × 10⁸) / (1.5 × 10⁻⁵)
f = 2 × 10¹³ Hz
Answer: 2 × 10¹³ Hz
Q2: What is the frequency of the 193-nm ultraviolet radiation used in laser eye surgery?
Given:
Wavelength, λ = 193 nm = 193 × 10⁻⁹ m = 1.93 × 10⁻⁷ m
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
f = c / λ
Calculation:
f = (3 × 10⁸) / (1.93 × 10⁻⁷)
f = (3 × 10⁸) / (1.93 × 10⁻⁷)
f = 1.55 × 10¹⁵ Hz
Answer: 1.55 × 10¹⁵ Hz
Wavelength, λ = 193 nm = 193 × 10⁻⁹ m = 1.93 × 10⁻⁷ m
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
f = c / λ
Calculation:
f = (3 × 10⁸) / (1.93 × 10⁻⁷)
f = (3 × 10⁸) / (1.93 × 10⁻⁷)
f = 1.55 × 10¹⁵ Hz
Answer: 1.55 × 10¹⁵ Hz
Q3: Calculate the wavelength of 100-MHz radio waves used in an MRI unit?
Given:
Frequency, f = 100 MHz = 100 × 10⁶ Hz = 1 × 10⁸ Hz
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
λ = c / f
Calculation:
λ = (3 × 10⁸) / (1 × 10⁸)
λ = 3 m
Answer: 3 m
Frequency, f = 100 MHz = 100 × 10⁶ Hz = 1 × 10⁸ Hz
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
λ = c / f
Calculation:
λ = (3 × 10⁸) / (1 × 10⁸)
λ = 3 m
Answer: 3 m
Q4: The distance from earth to sun is 1.49 × 10¹¹ meters. How long a radio pulse radiated from the sun takes to reach on the earth?
Given:
Distance, d = 1.49 × 10¹¹ m
Speed of light, c = 3 × 10⁸ m/s
Formula: t = d / c
Calculation:
t = (1.49 × 10¹¹) / (3 × 10⁸)
t = (1.49 / 3) × 10³
t = 0.49667 × 10³
t = 496.67 s
Answer: 496.67 seconds
Distance, d = 1.49 × 10¹¹ m
Speed of light, c = 3 × 10⁸ m/s
Formula: t = d / c
Calculation:
t = (1.49 × 10¹¹) / (3 × 10⁸)
t = (1.49 / 3) × 10³
t = 0.49667 × 10³
t = 496.67 s
Answer: 496.67 seconds
Q5: Distances in space are often measured in units of light-years, the distance light travels in one year. Find the distance in kilometers in a light-year?
Given:
Speed of light, c = 3 × 10⁸ m/s
Time, t = 1 year
Conversion:
1 year = 365 days × 24 hours × 3600 seconds
1 year = 365 × 24 × 3600 = 31,536,000 seconds
1 year = 3.1536 × 10⁷ s
Formula: Distance = c × t
Calculation:
Distance = (3 × 10⁸) × (3.1536 × 10⁷)
Distance = 9.4608 × 10¹⁵ m
Distance in km = 9.4608 × 10¹² km
Answer: 9.46 × 10¹² km
Speed of light, c = 3 × 10⁸ m/s
Time, t = 1 year
Conversion:
1 year = 365 days × 24 hours × 3600 seconds
1 year = 365 × 24 × 3600 = 31,536,000 seconds
1 year = 3.1536 × 10⁷ s
Formula: Distance = c × t
Calculation:
Distance = (3 × 10⁸) × (3.1536 × 10⁷)
Distance = 9.4608 × 10¹⁵ m
Distance in km = 9.4608 × 10¹² km
Answer: 9.46 × 10¹² km
Q6: What is the frequency of green light with a wavelength of 5.5 × 10⁻⁷ m?
Given:
Wavelength, λ = 5.5 × 10⁻⁷ m
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
f = c / λ
Calculation:
f = (3 × 10⁸) / (5.5 × 10⁻⁷)
f = (3 × 10⁸) / (5.5 × 10⁻⁷)
f = (3/5.5) × 10¹⁵
f = 0.545 × 10¹⁵
f = 5.45 × 10¹⁴ Hz
Answer: 5.45 × 10¹⁴ Hz
Wavelength, λ = 5.5 × 10⁻⁷ m
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
f = c / λ
Calculation:
f = (3 × 10⁸) / (5.5 × 10⁻⁷)
f = (3 × 10⁸) / (5.5 × 10⁻⁷)
f = (3/5.5) × 10¹⁵
f = 0.545 × 10¹⁵
f = 5.45 × 10¹⁴ Hz
Answer: 5.45 × 10¹⁴ Hz
Q7: A typical household microwave oven operates at a frequency of 2.45-GHz. What is the wavelength of this radiation?
Given:
Frequency, f = 2.45 GHz = 2.45 × 10⁹ Hz
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
λ = c / f
Calculation:
λ = (3 × 10⁸) / (2.45 × 10⁹)
λ = (3 × 10⁸) / (2.45 × 10⁹)
λ = (3/2.45) × 10⁻¹
λ = 1.224 × 10⁻¹
λ = 0.1224 m
λ = 122.4 mm
Answer: 0.1224 m or 122.4 mm
Frequency, f = 2.45 GHz = 2.45 × 10⁹ Hz
Speed of light, c = 3 × 10⁸ m/s
Formula: c = fλ
λ = c / f
Calculation:
λ = (3 × 10⁸) / (2.45 × 10⁹)
λ = (3 × 10⁸) / (2.45 × 10⁹)
λ = (3/2.45) × 10⁻¹
λ = 1.224 × 10⁻¹
λ = 0.1224 m
λ = 122.4 mm
Answer: 0.1224 m or 122.4 mm
