Problem
Base your answer to the question on the information below. A glass tube is filled with hydrogen gas at low pressure. An electric current is passed through the gas, causing it to emit light. This light is passed through a prism to separate the light into the bright, colored lines of hydrogen's visible spectrum. Each colored line corresponds to a particular wavelength of light. One of hydrogen's spectral lines is red light with a wavelength of 656 nanometers. Tubes filled with other gases produce different bright-line spectra that are characteristic of each kind of gas. These spectra have been observed and recorded. A student measured the wavelength of hydrogen's visible red spectral line to be 647 nanometers. Which is a correct numerical setup for calculating the student's percent error? 1. \( \% \) error \( =\frac{656 \mathrm{~nm}-647 \mathrm{~nm}}{656 \mathrm{~nm}} \times 100 \) 2. \( \% \) error \( =\frac{656 \mathrm{~nm}-647 \mathrm{~nm}}{647 \mathrm{~nm}} \times 100 \) 3. \( \% \) error \( =\frac{647 \mathrm{~nm}-656 \mathrm{~nm}}{656 \mathrm{~nm}} \times 100 \) 4. \( \% \) error \( =\frac{647 \mathrm{~nm}-656 \mathrm{~nm}}{647 \mathrm{~nm}} \times 100 \)
Solution
Step 1 ：\( \% \) error \( =\frac{\textit{accepted value} - \textit{measured value}}{\textit{accepted value}} \times 100 \)
Step 2 ：\( \% \) error \( =\frac{656 \mathrm{~nm}-647 \mathrm{~nm}}{656 \mathrm{~nm}} \times 100 \)
Step 3 ：\( \% \) error \( =\frac{9 \mathrm{~nm}}{656 \mathrm{~nm}} \times 100 \)
