Answer
The color of visible light emitted by barium is green.
Work Step by Step
The energy of a photon is directly related to its frequency and inversely related to its wavelength. The visible light spectrum ranges from approximately 400 nm (violet) to 700 nm (red). Using the equation \( E = hf = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant, \( f \) is the frequency, \( c \) is the speed of light, and \( \lambda \) is the wavelength, we can calculate the wavelength of the light emitted by barium.
First, we can calculate the frequency of the light using the energy of the photon:
\[ E = hf \]
\[ f = \frac{E}{h} = \frac{3.59 \times 10^{-19} \mathrm{~J}}{6.626 \times 10^{-34} \mathrm{~J\cdot s}} \]
\[ f \approx 5.41 \times 10^{14} \mathrm{~Hz} \]
Next, we can use the speed of light to calculate the wavelength:
\[ c = f\lambda \]
\[ \lambda = \frac{c}{f} = \frac{3.00 \times 10^8 \mathrm{~m/s}}{5.41 \times 10^{14} \mathrm{~Hz}} \]
\[ \lambda \approx 555 \mathrm{~nm} \]
The wavelength of approximately 555 nm corresponds to green light. Therefore, the color of visible light emitted by barium is green.
