Question

what is the wavelength of light (in meters) that has a frequency of 5.71×10^7 1/s? c=λ × v c=3.00×10^8 m/s

Explanation:

Step1: Rearrange the formula

Given \(c = \lambda\times v\), we can solve for \(\lambda\) by \(\lambda=\frac{c}{v}\)

Step2: Substitute the values

We know \(c = 3.00\times 10^{8}\frac{m}{s}\) and \(v=5.71\times 10^{7}\frac{1}{s}\)

Substitute into \(\lambda=\frac{c}{v}\), we get \(\lambda=\frac{3.00\times 10^{8}\frac{m}{s}}{5.71\times 10^{7}\frac{1}{s}}\)

Step3: Calculate the result

Using the rule of dividing exponents \(a^{m}\div a^{n}=a^{m - n}\), \(\frac{3.00}{5.71}\approx0.525\) and \(10^{8}\div10^{7}=10^{8 - 7}=10^{1}\)

So \(\lambda=0.525\times10^{1}m = 5.25m\)

Answer:

\(5.25m\)