1) Frequency: [tex]3.29\cdot 10^{15}Hz[/tex]
the energy of the photon absorbed must be equal to the ionization enegy of the atom, which is
[tex]E=2.18 aJ=2.18\cdot 10^{-18} J[/tex]
The energy of a photon is given by
[tex]E=hf[/tex]
where [tex]h=6.63\cdot 10^{-34}Js[/tex] is the Planck's constant. By using the energy written above and by re-arranging thsi formula, we can calculate the frequency of the photon:
[tex]f=\frac{E}{h}=\frac{2.18\cdot 10^{-18} J}{6.63\cdot 10^{-34} Js}=3.29\cdot 10^{15} Hz[/tex]
2) Wavelength: 91.2 nm
The wavelength of the photon can be found from its frequency, by using the following relationship:
[tex]\lambda=\frac{c}{f}[/tex]
where [tex]c=3\cdot 10^8 m/s[/tex] is the speed of light and f is the frequency. Substituting the frequency, we find
[tex]\lambda=\frac{3\cdot 10^8 m/s}{3.29\cdot 10^{15}Hz}=9.12\cdot 10^{-8} m=91.2 nm[/tex]
