Question

relating wavelength and frequency
order the electromagnetic waves from lowest frequency (1) to highest (4).
gamma:
infrared:
x - ray:
visible light:

Explanation:

Step1: Recall the relationship between wavelength and frequency

The formula \(c = \lambda f\) (where \(c\) is the speed of light, \(\lambda\) is wavelength, and \(f\) is frequency) shows that frequency \(f=\frac{c}{\lambda}\). Since \(c\) is a constant (\(c = 3\times10^{8}\space m/s\)), frequency is inversely proportional to wavelength.

Step2: Compare the wavelengths

• Infrared has the longest wavelength range (\(7\times 10^{-7}\space m\) to \(1\times 10^{-3}\space m\)). Using \(f=\frac{c}{\lambda}\), it will have the lowest frequency.
• Visible light has a shorter wavelength range (\(4\times 10^{-7}\space m\) to \(7\times 10^{-7}\space m\)) than infrared. So its frequency is higher than infrared.
• X - ray has a shorter wavelength range (\(1\times 10^{-11}\space m\) to \(1\times 10^{-8}\space m\)) than visible light. So its frequency is higher than visible light.
• Gamma rays have the shortest wavelength (\(<1\times 10^{-11}\space m\)). Using \(f = \frac{c}{\lambda}\), it will have the highest frequency.

Answer:

Infrared: 1, Visible light: 2, X - ray: 3, Gamma: 4