Question

1. which has the longer wavelength? light with a frequency of 7.32x10¹⁴hz or light with a frequency of 6.0x10¹⁴hz?

Explanation:

Step1: Recall the relationship between wavelength and frequency

The speed of light \(c\) is related to frequency \(f\) and wavelength \(\lambda\) by the formula \(c = f\lambda\), where \(c = 3\times10^{8}\text{ m/s}\) (constant). So, \(\lambda=\frac{c}{f}\).

Step2: Analyze the inverse - relationship

Since \(\lambda=\frac{c}{f}\) and \(c\) is constant, wavelength \(\lambda\) is inversely proportional to frequency \(f\). That is, when \(f\) is smaller, \(\lambda\) is larger.

Step3: Compare the two frequencies

We have \(f_1 = 7.32\times 10^{14}\text{ Hz}\) and \(f_2=6.0\times 10^{14}\text{ Hz}\). Since \(6.0\times 10^{14}\text{ Hz}<7.32\times 10^{14}\text{ Hz}\) (i.e., \(f_2 < f_1\))

Answer:

Light with a frequency of \(6.0\times 10^{14}\text{ Hz}\) has a longer wavelength.