Question

When a firework star bursts, the color of the "stars" is determined by the chemical compounds in the firework. The wavelengths for different colors in the spectrum are shown below. $$\begin{array}{|l|l|} \hline \text { Ultraviolet } & w<400 \\ \hline \text { Violet } & 400 \leq w<424 \\ \hline \text { Blue } & 424 \leq w<491 \\ \hline \text { Green } & 491 \leq w<575 \\ \hline \text { Yellow } & 575 \leq w<585 \\ \hline \text { Orange } & 585 \leq w<647 \\ \hline \text { Red } & 647 \leq w<700 \\ \hline \text { nfrared } & 700 \leq w \\ \hline \end{array}$$ A firework star contains a sodium compound. When it is burned. the compound emits light at wavelengths given by \(|w-600|<5\) Determine the color of the star.

Short answer

The color of the star is Orange.

Step-by-step solution

Determine the Range of Wavelengths Emitted by Star

First, the inequality \(|w-600|<5\) can be re-arranged to find the range in which \(w\) lies. We must rewrite the absolute value inequality in terms of compound inequalities. This can be done by solving the equation separately for the positive and negative forms. This gives us \(595 < w < 605\). So, the wavelengths emitted by the firework star fall within this range.

Match the Range of Wavelengths to the Colors

Now, using the table given, we can see which color's wavelength range includes the wavelengths emitted by the star (between 595 and 605). Looking at the table, we can see that this range falls within the wavelength range for the colors Orange and Yellow.

Determine the Star Color

The wavelength range \(595 < w < 605\) means the firework star is emitting light within the colors Orange and Yellow. As the color of a star is determined by the majority color it emits, and as this range is mostly within the Orange section (from 595 to 601), Orange is the color of the star.