Question 4 - Science Practice Test for the ACT

One of the energy sources that Gwen used in her experiment was a dust cloud, as it emits infrared radiation. The radiation emitted from the dust cloud had a frequency of 0.000075 Hz. According to Figure 2, what was the wavelength of the infrared radiation?

Note: On both attached graphs in “Read Text”, the x-axis should be labeled “wavelength” and the y-axis should be labeled “Hz”.

Energy travels through space by electromagnetic radiation (Table 1). There are many forms of radiant energy, such as sunlight, microwave oven energy, X-rays, and heat from a fireplace. All forms of electromagnetic radiation exhibit wavelike behaviour and travel at the speed of light (c) in a vacuum. Wavelength, frequenc and speed are the three primary characteristics of waves. Wavelength (λ) is the distance between two consecutive peaks in a wave. Frequency (ν) is the number of waves (cycles) per second that pass a given point in space. There is an inverse relationship between wavelength and frequency—short wavelength radiation has a high frequency, whereas long wavelength radiation has a low frequency.

Table 1: Classification of Electromagnetic Radiation

Types of Radiation Wavelength (meters)
in Increasing Order
Gamma rays \(1 \cdot 10^{-12}\)
X-rays \(1 \cdot 10^{-10}\)
Ultraviolet rays \(1 \cdot 10^{-8}\)
Visible light spectrum \(4 \cdot 10^{-7} - 7 \cdot 10^{-7}\)
Infrared \(1 \cdot 10^{-4}\)
Microwaves \(1 \cdot 10^{-2}\)
Radio waves  
-FM \(1\)
-Shortwave \(1 \cdot 10^2\)
-AM \(1 \cdot 10^4\)

Alfred and Gwen ran experiments to measure the wavelengths of various types of energy sources. Alfred used energy sources that emit microwave radiation, whereas Gwen used sources that emit infrared radiation. After determining the wavelengths of the energy sources used, they calculated the frequency of radiation for each source using the following formula for the speed of light:

c = λν, where
λ = wavelength [meters (m)]
ν = frequency [cycles per second = 1/s = Hertz (Hz)]
c = speed of light (m/s) = 2.9979 x 108 m/s

Frequency can be calculated by rearranging this equation to solve for frequency, ν = c/λ. Alfred and Gwen plotted frequency as a function of wavelength and the resulting graphs are shown in Figures 1 and 2.

Figure 1: Alfred’s Experiment—Microwave Radiation
1-4-(-a)-a-c-t-science-p-q.png

Figure 2: Gwen’s Experiment—Infrared Radiation
1-4-(-b)-a-c-t-s-c-i-e-n-c-e-infrared-radiation.png

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