Question

electromagnetic spectrum practice

1. according to the diagram, radio waves have wavelengths of ______ m
2. according to the diagram, gamma rays have wavelengths of ______ m
3. which one has the smallest wavelength?

a. radio
b. gamma
c. ultraviolet

1. which of the following waves carries the most energy?

a. visible light
b. ultraviolet
c. microwaves
fill in the blanks below with the words \increases\ or \decreases.\

1. as the wavelength of a wave increases, its energy ______
2. as the frequency of a wave increases, its energy ______
3. energy decreases as wavelength ______

choose the correct answer

1. if you have a telescope that can detect frequencies of around $10^8$, what kind of wave could you observe?

a. microwave
b. ultraviolet
c. visible light
d. x-ray

1. a wave that has a frequency higher than $10^9$ but less than $10^{13}$ could be a(n)...

a. infrared wave
b. gamma wave
c. radio wave

Explanation:

Step1: Recall radio wave wavelength range

Radio waves have wavelengths of $\geq 10^{-1}\ \text{m}$ (or typically stated as $10^{-1}\ \text{m}$ to $10^{4}\ \text{m}$; standard value is $\geq 10^{-1}\ \text{m}$)

Step2: Recall gamma ray wavelength range

Gamma rays have wavelengths of $\leq 10^{-11}\ \text{m}$ (or $10^{-16}\ \text{m}$ to $10^{-11}\ \text{m}$; standard value is $\leq 10^{-11}\ \text{m}$)

Step3: Identify smallest wavelength wave

Electromagnetic spectrum order (smallest to largest wavelength): Gamma < UV < Radio

Step4: Relate energy to frequency/wavelength

Energy formula: $E=h
u=\frac{hc}{\lambda}$, where $h$=Planck's constant, $
u$=frequency, $\lambda$=wavelength, $c$=speed of light. Higher frequency/shorter wavelength = higher energy.

Step5: Match frequency to wave type

Microwaves: $10^{8}-10^{12}\ \text{Hz}$; UV: $10^{15}-10^{17}\ \text{Hz}$; Visible: $4\times10^{14}-7.5\times10^{14}\ \text{Hz}$; X-ray: $10^{17}-10^{20}\ \text{Hz}$; Infrared: $10^{12}-10^{14}\ \text{Hz}$; Gamma: $>10^{19}\ \text{Hz}$; Radio: $<10^{9}\ \text{Hz}$

Step6: Fill energy-wavelength/frequency blanks

From $E=\frac{hc}{\lambda}$, longer $\lambda$ = lower $E$; higher $
u$ = higher $E$.

Step7: Solve frequency range question

$10^{9}<\text{frequency}<10^{13}$ matches infrared's range.

Answer:

1. $\geq 10^{-1}$ (or $10^{-1}$ to $10^{4}$)
2. $\leq 10^{-11}$ (or $10^{-16}$ to $10^{-11}$)
3. b. Gamma
4. b. Ultraviolet
5. decreases
6. increases
7. increases
8. a. Microwave
9. a. Infrared wave