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 barium chlorate. When it is burned, barium chlorate emits light at wavelengths given by \(|w-519.5|<12.5\) What color is the star?

Short answer

The color of the star is Green.

Step-by-step solution

Understand the Wavelength Equation

Firstly, we need to understand what the given equation \(|w-519.5|<12.5\) implies. The absolute value implies that the wavelength, 'w', can either be greater or less than 519.5. In simple words, our wavelength can either be 12.5 less than 519.5 or 12.5 more than 519.5.

Calculate the Range of Wavelengths

Subtracting 12.5 from 519.5, we get 507. Similarly, adding 12.5 to 519.5, we get 532. So the wavelength range for the light emitted by barium chlorate is\(507 \leq w < 532\).

Compare Wavelength Range with the Colors Spectrum

Now, we will match our calculated wavelength range with the given color spectrum. On comparing, we can see that our wavelength range falls under the category of 'Green' color which is from 491 to 575. Therefore, the light emitted will be 'Green'.