In fireworks displays, light of a given wavelength indicates the presence of a particular element. What are the frequency and color of the l

Question

In fireworks displays, light of a given wavelength indicates the presence of a particular element. What are the frequency and color of the light associated with each of the following?

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Adela 5 years 2021-09-04T23:04:25+00:00 1 Answers 131 views 0

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  1. thugiang
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    2021-09-04T23:06:06+00:00
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    Answer:

    The four wavelengths of the problem are not given. Here they are:

    a) Li^+,\lambda=671 nm

    b) Cs^+, \lambda=456 nm

    c) Ca^{2+}, \lambda=649 nm

    d) Na^+, \lambda=589 nm

    The relationship between wavelength and frequency of light wave is

    f=\frac{c}{\lambda}

    where

    f is the frequency

    c=3.0\cdot 10^8 m/s is the speed of light

    \lambda is the wavelength

    For case a), \lambda=671 nm = 6.71\cdot 10^{-7}m (corresponds to red color), so its frequency is

    f=\frac{3\cdot 10^8}{6.71\cdot 10^{-7}}=4.47\cdot 10^{14}Hz

    For case b), \lambda=456 nm = 4.56\cdot 10^{-7}m (corresponds to blue color), so its frequency is

    f=\frac{3\cdot 10^8}{4.56\cdot 10^{-7}}=6.58\cdot 10^{14}Hz

    For case c), \lambda=649 nm = 6.49\cdot 10^{-7}m (corresponds to red color), so its frequency is

    f=\frac{3\cdot 10^8}{6.49\cdot 10^{-7}}=4.62\cdot 10^{14}Hz

    For case d), \lambda=589 nm = 5.89\cdot 10^{-7}m (corresponds to yellow color), so its frequency is

    f=\frac{3\cdot 10^8}{5.89\cdot 10^{-7}}=5.09\cdot 10^{14}Hz

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