Question

1. the energy of violet light is approximately twice that of red light. how do the wavelengths of violet and red light compare? the wavelength of violet light is approximately half that of red light. the wavelength of violet light is approximately twice that of red light. the wavelength of violet light is the same as that of red light. the wavelength of violet light is sometimes greater than and sometimes less than that of red light.

Explanation:

Step1: Recall energy - wavelength relation

The energy of a photon is given by $E = h
u=\frac{hc}{\lambda}$, where $h$ is Planck's constant, $
u$ is the frequency, $c$ is the speed of light and $\lambda$ is the wavelength. Energy and wavelength are inversely proportional.

Step2: Analyze the given energy ratio

If the energy of violet light $E_{v}$ is approximately twice the energy of red light $E_{r}$, i.e., $E_{v}\approx2E_{r}$. Using $E=\frac{hc}{\lambda}$, we have $\frac{E_{v}}{E_{r}}=\frac{\lambda_{r}}{\lambda_{v}}$. Since $E_{v}\approx2E_{r}$, then $\frac{\lambda_{r}}{\lambda_{v}}\approx2$, or $\lambda_{v}\approx\frac{1}{2}\lambda_{r}$.

Answer:

The wavelength of violet light is approximately half that of red light.