Respuesta :
Explanation:
Energy levels of a hypothetical atom:
[tex]E_4 =-1.21\times 10^{-19} J [/tex]
[tex]E_3 =-5.71\times 10^{-19} J [/tex]
[tex]E_2 =-1.05\times 10^{-18} J [/tex]
[tex]E_1 =-1.55\times 10^{-18} J [/tex]
a) Wavelength of the photon needed to excite an electron from [tex]E_1[/tex] to [tex]E_4[/tex].
Energy difference between forth and first energy level =
[tex]E=E_4-E_1=(-1.21\times 10^{-19} J )-(-1.55\times 10^{-18} J)=1.429\times 10^{-18} J[/tex]
[tex]E=\frac{hc}{\lambda }[/tex]
[tex]\lambda =\frac{hc}{E}=\frac{(6.634\times 10^{-34}Js)\times (3\times 10^8m/s)}{1.429\times 10^{-18} J}[/tex]
[tex]=1.392\times 10^{-7} m=139.2 nm[/tex]
139.2 nm is the wavelength of the photon needed to excite an electron from [tex]E_1[/tex] to [tex]E_4[/tex].
b) Energy of a photon in order to excite an electron from [tex]E_2[/tex] to [tex]E_3[/tex].
Energy difference between third and second energy level =
[tex]E=E_3-E_2=(-5.71\times 10^{-19} J)-(-1.05\times 10^{-18} J)=4.79\times 10^{-19} J[/tex]
[tex]4.79\times 10^{-19} J[/tex] is the energy a photon to excite an electron from [tex]E_2[/tex] to [tex]E_3[/tex].
c) Electron drops from the [tex]E_3[/tex] level to the [tex]E_1[/tex] level
Energy difference between third and first energy level =
[tex]E=E_3-E_1=(-5.71\times 10^{-19} J )-(-1.55\times 10^{-18} J)=9.79\times 10^{-19} J[/tex]
[tex]E=\frac{hc}{\lambda }[/tex]
[tex]\lambda =\frac{hc}{E}=\frac{(6.634\times 10^{-34}Js)\times (3\times 10^8m/s)}{9.79\times 10^{-19} J}[/tex]
[tex]=2.033\times 10^{-7} m=203.3 nm[/tex]
202.3 nm is the wavelength of the photon of emitted.
