Question

What is the longest wavelength light capable of ionizing a hydrogen atom in the ground state?

Answer 1

Answer:

$9.12\cdot 10^{-8} m$

Explanation:

The energy needed to ionize a hydrogen atom in the ground state is:

$E=13.6 eV= 2.18\cdot 10^{-18}J$

The energy of the photon is related to the wavelength by

$E=\frac{hc}{\lambda}$

where

h is the Planck constant

c is the speed of light

$\lambda$ is the wavelength

Solving the formula for the wavelength, we find

$\lambda=\frac{hc}{E}=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{2.18\cdot 10^{-18}J}=9.12\cdot 10^{-8} m$