Problem: Complete this table for visible lightWavelength (nm)          Frequency(s-1)          Energy per photon (J)          Colora. 713.7                          __________               _____________                  __________   b. ______                     5.376 x 10 14                     _____________                    __________  c.  ______                    __________                _____________                     yellowd. ______                     __________               4.415 x 10 -19                           __________  

FREE Expert Solution

To complete the given table for visible light:

$\boxed{\mathbf{E}\mathbf{=}\mathbf{hv}} \left(1\right)$

where:

h = Planck’s constant (6.626 × 10^–34 J • s)

v = frequency (in s^–1)

$\boxed{\mathbf{\lambda }\mathbf{=}\frac{\mathbf{c}}{\mathbf{v}}} \left(2\right)$

where:

c = speed of light (3.0 × 10⁸ m/s)

$\boxed{\mathbf{E}\mathbf{=}\frac{\mathbf{hc}}{\mathbf{\lambda }}} \left(3\right)$

    Color            wavelength, nm

Violet              380 – 450 nm

Blue                450 – 495 nm

Green             495 – 570 nm

Yellow             570 – 590 nm

Orange           590 – 620 nm

Red                 620 – 750 nm

a) Find v, E, color of light

$$\begin{gathered} \cancel{\mathbf{\lambda }}\mathbf{\left(}\frac{\mathbf{v}}{\cancel{\mathbf{\lambda }}}\mathbf{\right)}\mathbf{=}\frac{\mathbf{c}}{\cancel{\mathbf{v}}}\mathbf{\left(}\frac{\cancel{\mathbf{v}}}{\mathbf{\lambda }}\mathbf{\right)} \\ \mathbf{\nu }\mathbf{=}\frac{\mathbf{c}}{\mathbf{\lambda }} \\ \mathbf{\nu }\mathbf{=}\frac{\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}{\displaystyle \frac{\cancel{\mathbf{m}}}{\mathbf{s}}}}{\mathbf{713}\mathbf{.}\mathbf{7}\mathbf{ }\cancel{\mathbf{nm}}\mathbf{\times }\frac{{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{ }\cancel{\mathbf{m}}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{nm}}}} \end{gathered}$$

v = 4.203 × 10¹⁴ s^-1

            

$\mathbf{E}\mathbf{=}\mathbf{(}\mathbf{6}\mathbf{.}\mathbf{626}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{34}}\mathbf{ }\mathbf{J}\mathbf{·}\cancel{\mathbf{s}}\mathbf{)}\mathbf{(}\mathbf{4}\mathbf{.}\mathbf{203}\mathbf{\times }{\mathbf{10}}^{\mathbf{14}}\cancel{{\mathbf{s}}^{\mathbf{-}\mathbf{1}}}\mathbf{)}$