Question

you know that because radio waves are part of the electromagnetic spectrum, their speed, frequency, and wavelength are related by the formula c = λν.

1. solve for the unknown

solve the equation relating the speed, frequency, and wavelength of an electromagnetic wave for wavelength (λ).
if c = λν, then λ =
substitute c and the frequency of the radio wave, ν, into the equation. note that hertz is equivalent to 1/s or s⁻¹.
λ =
divide the values to determine wavelength, λ and cancel units as required.
λ =
science notebook - electrons in atoms
62

Explanation:

Step1: Rearrange the formula

Given \( c = \lambda
u\), to solve for \(\lambda\), divide both sides of the equation by \(
u\).

$$ \lambda=\frac{c}{ u} $$

Step2: Substitute values (assuming \(c = 3\times10^{8}\space m/s\) and \(

u\) is given, but since no specific values for \(c\) and \(
u\) are provided in the problem statement beyond the formula manipulation, the general form after substitution would still be \(\lambda=\frac{c}{
u}\) where \(c\) is the speed of light (\(3\times 10^{8}\space m/s\) for electromagnetic waves in vacuum) and \(
u\) is the frequency in \(Hz\) (or \(s^{-1}\)).

Step3: Unit cancellation (for general understanding)

The units of \(c\) is \(m/s\) and of \(
u\) is \(s^{-1}\). When we divide \(m/s\) by \(s^{-1}\) (\(\frac{m/s}{s^{-1}}=\frac{m\times s}{s}=m\)), the resulting unit for \(\lambda\) is meters (\(m\)), which is the unit for wavelength.

Answer:

If \(c = \lambda
u\), then \(\lambda=\frac{c}{
u}\). After substitution (with \(c\) as the speed of light for electromagnetic waves in vacuum, \(c = 3\times 10^{8}\space m/s\) and \(
u\) as frequency) and unit - cancellation (since \(Hz=s^{-1}\)), \(\lambda=\frac{3\times 10^{8}\space m/s}{
u}\) (where \(
u\) is in \(Hz\) or \(s^{-1}\)).