Chapter 7

For each relationship below, indicate whether the two variables (indicated in bold) are proportional or inversely proportional: a) \(\quad \mathbf{y}=5 \mathbf{x}\) b) \(\quad \mathbf{p}=325 / \mathbf{v}\) c) For a given amount of force, if the mass of a car is doubled, the acceleration of the car is cut in half.

The frequency \((f)\) of a wave is defined as the number of wavelengths per second which travel past a given point. a) For a wave traveling at a given speed, \(c\), how does the frequency depend on the wavelength, if at all? b) Provide a mathematical expression showing the relationship between \(f\), \(\lambda\), and \(c\) for a wave. (Hint: consider how you determined answers to CTQs 4 and \(4 b\) ).

a) Write the mathematical equation that relates the energy of a photon and its wavelength. b) Is the energy of a photon proportional or inversely proportional to \(\lambda\) ? $$ \begin{array}{ll} \hline \text { Region } & \text { Wavelength Range } \\ \hline \text { radiowave } & 3 \mathrm{~km}-30 \mathrm{~cm} \\ \text { microwave } & 30 \mathrm{~cm}-1 \mathrm{~mm} \\ \text { infrared (IR) } & 1 \mathrm{~mm}-800 \mathrm{~nm} \\ \text { visible (VIS) } & 800 \mathrm{~nm}-400 \mathrm{~nm} \\ \text { ultraviolet (UV) } & 400 \mathrm{~nm}-10 \mathrm{~nm} \\ \text { X-ray } & 10 \mathrm{~nm}-0.1 \mathrm{~nm} \\ \text { gamma ray } & <0.1 \mathrm{~nm} \\ \hline \end{array} $$ $$ \begin{array}{ccc} \hline \hline \begin{array}{c} \text { Wavelength } \\ (\mathrm{nm}) \end{array} & \begin{array}{c} \text { Frequency } \\ \left(10^{14} \mathrm{~s}^{-1}\right) \end{array} & \begin{array}{c} \text { Energy } \\ \left(10^{-19} \mathrm{~J}\right) \end{array} \\ \hline 333.1 & 9.000 & 5.963 \\ 499.7 & 6.000 & 3.976 \\ 999.3 & 3.000 & 1.988 \\ \hline \end{array} $$