Answer:
[tex]9.12\cdot 10^{-8} m[/tex]
Explanation:
The energy needed to ionize a hydrogen atom in the ground state is:
[tex]E=13.6 eV= 2.18\cdot 10^{-18}J[/tex]
The energy of the photon is related to the wavelength by
[tex]E=\frac{hc}{\lambda}[/tex]
where
h is the Planck constant
c is the speed of light
[tex]\lambda[/tex] is the wavelength
Solving the formula for the wavelength, we find
[tex]\lambda=\frac{hc}{E}=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{2.18\cdot 10^{-18}J}=9.12\cdot 10^{-8} m[/tex]
