Question

in a discharge tube, helium atoms emit light as they undergo transitions from one energy level to another that is 3.378 x 10 - 19 j lower in energy. calculate the wavelength of the light emitted and by referring to the figure to the right, predict the color of the line in the discharge spectrum. wavelength = m color:

Explanation:

Step1: Use the formula \(E = h

u=\frac{hc}{\lambda}\)
We know that \(E = 3.378\times10^{- 19}\space J\), \(h = 6.626\times10^{-34}\space J\cdot s\), and \(c = 3\times10^{8}\space m/s\). Rearranging the formula \(\lambda=\frac{hc}{E}\)

Step2: Substitute the values

\(\lambda=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{3.378\times 10^{-19}}\)

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Step3: Convert to nanometers

Since \(1\space m=10^{9}\space nm\), \(\lambda = 5.885\times10^{-7}\times10^{9}\space nm = 588.5\space nm\)
Looking at the color - wavelength chart, \(588.5\space nm\) corresponds to the yellow color.

Answer:

Color: Yellow, Wavelength \(=5.89\times 10^{-7}\space m\) (approximate value considering significant figures, original calculation gives \(5.885\times10^{-7}\space m\) and rounding to three significant figures as \(h = 6.63\times10^{-34}\), \(c = 3.00\times10^{8}\) and \(E = 3.38\times10^{-19}\) gives \(\lambda=\frac{6.63\times10^{-34}\times3.00\times10^{8}}{3.38\times10^{-19}}=\frac{19.89\times10^{-26}}{3.38\times10^{-19}}=\frac{19.89}{3.38}\times10^{-7}\approx5.89\times10^{-7}\space m\))