Consider the electronic transition from n = 7 to n = 4 in the hydrogen atom. is light absorbed or emitted? calculate the energy, the frequency and wavelength (nm) of the photon involved.

Respuesta :

Light is emitted, energy is  9.16 × [tex]10^{-20}[/tex] J , frequency is 1.38 × [tex]10^{-14}[/tex] [tex]s^-[/tex]    

and wavelength is  2.17 × [tex]10^{-6}[/tex] m      

Explanation

n = 7 → n = 4

higher → lower

Light is emitted

[tex]\Delta[/tex]E = [tex]\frac{-13.6}{7^2} - (\frac{-13.6}{4^2})[/tex]

[tex]\Delta[/tex]E = 0.85 - 0.277

     = 0.572 eV

[tex]\Delta[/tex]E = 9.16 × [tex]10^{-20}[/tex] J              -> [energy calculated]

[tex]\Delta[/tex]E = hv           (h is Planck's constant and v is frequency)

v = [tex]\frac{\Delta E}{h}[/tex]  = [tex]\frac{9.16 * 10^{-20}}{6.626 * 10^{-39}}[/tex]

v = 1.38 × [tex]10^{-14}[/tex] [tex]s^-[/tex]                 ->[frequency calculated]

[tex]\Delta[/tex]E = [tex]\frac{hc}{\Lambda}[/tex]            (c is speed of light)

[tex]\Lambda[/tex] = [tex]\frac{hc}{\Delta E}[/tex]

[tex]\Lambda[/tex] = [tex]\frac{6.626 * 10^{-34} . 3*10^8 m/s}{9.16 *10^{-20 J} }[/tex]

[tex]\Lambda[/tex] = 2.17 × [tex]10^{-6}[/tex] m                    ->[wavelength calculated]

What is energy?

Energy, according to scientists, is the capacity for work. The ability to transform energy from one form to another and use it to perform tasks is what makes modern civilization possible. People utilize energy to travel by foot and bicycle, drive vehicles on land and in water, prepare meals on stoves, create ice in freezers, illuminate our homes and workplaces, create goods, and launch people into space.

Energy comes in a wide variety of forms, including:

  • Heat
  • Light
  • Motion
  • Electrical
  • Chemical
  • Gravitational

These energies can be divided into two categories for working energy:

  • Potential or stored energy
  • Kinetic or working energy

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