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Concept explainers
Interpretation:
The given table has to be completed.
Frequency | Wavelength | Energy of photon | Event |
8.7×1014 Hz | |||
3.3×10−19J | |||
300 MHz | |||
2.5 nm |
Concept Introduction:
The relationship between wavelength, frequency and
λ×ν=c
Where, λ is the wavelength, ν is the frequency of radiation and c is the speed of light.
Energy of a photon can be expressed mathematically as given below.
E=hν=hcλ
The wavelengths of electromagnetic radiation and their corresponding frequencies are given below in the table.
Radiation type | Frequency / (1014Hz) | Wavelength / (nm) | Energy of photon / (10−19J) |
x-rays and γ- rays | ≥103 | ≤3 | ≥103 |
Ultraviolet | 8.6 | 350 | 5.7 |
Visible light | |||
Violet | 7.1 | 420 | 4.7 |
Blue | 6.4 | 470 | 4.2 |
Green | 5.7 | 530 | 3.8 |
Yellow | 5.2 | 580 | 3.4 |
Orange | 4.8 | 620 | 3.2 |
Red | 4.3 | 700 | 2.8 |
Infrared | 3.0 | 1000 | 2.0 |
Microwaves and radio waves | ≤10−3 | ≥3×106 | ≤103 |
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Explanation of Solution
First row:
The frequency of the radiation is 8.7×1014 Hz.
The calculation of wavelength and energy of the radiation can be done as shown below.
λ=cν=3×108m/s8.7×1014s−1=3.44×10−7m=344 nmE=hcλ=(6.6×10−34J.s)×(3×108m/s)3.44×10−7m=5.7×10-19J
Second row:
The energy of the radiation is 3.3×10−19J.
The calculation of wavelength and frequency of the radiation can be done as shown below.
E=hcλλ=hcE=(6.6×10−34J.s)×(3×108m/s)3.3×10−19J=6×10-7m=600 nmν=cλ=3×108m/s600×10−9m=5.0×1014Hz
Third row:
The frequency of the radiation is 300 MHz.
The calculation of wavelength and energy of the radiation can be done as shown below.
λ=cν=3×108m/s300×106s−1=1 mE=hcλ=(6.6×10−34J.s)×(3×108m/s)1m=2×10-25J
Fourth row:
The wavelength of the radiation is 2.5 nm.
The calculation of frequencyand energy of the radiation can be done as shown below.
ν=cλ=3×108m/s2.5×10−9m=1.2×1017HzE=hν=(6.6×10−34J.s)×(1.2×1017s−1)=7.92×10-17J
Now, the given table can be filled up as given below.
Frequency | Wavelength | Energy of photon | Event |
8.7×1014 Hz | 344 nm | 5.7×10-19J | Sun tan |
5.0×1014Hz | 600 nm | 3.3×10−19J | Reading |
300 MHz | 1 m | 2×10-25J | Microwave popcorn |
1.2×1017Hz | 2.5 nm | 7.92×10-17J | Dental x-ray |
Want to see more full solutions like this?
Chapter 1 Solutions
Chemical Principles: The Quest for Insight
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