Question

periodic table
what is the wavelength of a light wave with a frequency of 2.5 × 10¹⁴ hz?
a. 7.5 × 10⁻⁶ m
b. 1.2 × 10⁻⁶ m
c. 1.2 × 10⁻⁵ m
d. 8.3 × 10⁵ m

Explanation:

Step1: Recall the wave - speed formula

The formula that relates the speed of light (\(c\)), wavelength (\(\lambda\)) and frequency (\(f\)) is \(c=\lambda f\), where the speed of light in a vacuum \(c = 3\times10^{8}\space m/s\). We need to solve for the wavelength \(\lambda\), so we can re - arrange the formula to \(\lambda=\frac{c}{f}\).

Step2: Substitute the values into the formula

We are given that \(f = 2.5\times10^{14}\space Hz\) and \(c = 3\times10^{8}\space m/s\). Substituting these values into the formula \(\lambda=\frac{c}{f}\), we get \(\lambda=\frac{3\times 10^{8}\space m/s}{2.5\times10^{14}\space Hz}\).
First, we can rewrite the division of the coefficients and the powers of 10 separately. \(\frac{3}{2.5}\times\frac{10^{8}}{10^{14}}\).
\(\frac{3}{2.5}=1.2\) and using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{10^{8}}{10^{14}}=10^{8-14}=10^{-6}\).
So, \(\lambda = 1.2\times10^{-6}\space m\).

Answer:

B. \(1.2\times 10^{-6}\space m\)