After applying sunscreen, Cherie lies in the summer sun to get a tan. The ultraviolet light responsible for tanning has a wavelength over 31

Question

After applying sunscreen, Cherie lies in the summer sun to get a tan. The ultraviolet light responsible for tanning has a wavelength over 310. nm, while the burning rays can range down to 280. nm. Which ultraviolet photons emit more energy, those that tan or those that burn?

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Diễm Thu 6 months 2021-08-17T07:02:09+00:00 1 Answers 4 views 0

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    2021-08-17T07:03:19+00:00

    Answer:

    The photons that burn, emit more energy.

    Explanation:

    The energy of the ultraviolet photons can be determined by means of the following equation:

    E = h\nu  (1)

    Equation 1 can be rewritten in terms of \lamba

    Since, c = \nu \lambda  

    \nu =  \frac{c}{\lambda}

    E = \frac{hc}{\lambda}  (2)

    Where h is the planck’s constant, c is the speed of light and \lambda is the wavelength.

    Case for the photon of with \lambda = 310nm

    \lambda = 310nm . \frac{1x10^{-9}m}{1nm}3.1x10^{-7}m

    E = \frac{hc}{\lambda}      

    E = \frac{(6.626x10^{-34}J.s)(3x10^{8}m/s)}{3.1x10^{-7}m}                                                        

    E = 6.412x10^{-19}J

    Case for the photon of with \lambda = 280nm

    \lambda = 280nm . \frac{1x10^{-9}m}{1nm}2.8x10^{-7}m

    E = \frac{hc}{\lambda}      

    E = \frac{(6.626x10^{-34}J.s)(3x10^{8}m/s)}{2.8x10^{-7}m}                                                        

    E = 7.099x10^{-19}J  

    Hence, the photons that burn, emit more energy.

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