Question

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

Answer 1

`9.12\cdot 10^(-8) m`

Step-by-step 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=(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=(hc)/(E)=((6.63\cdot 10^(-34) Js)(3\cdot 10^8 m/s))/(2.18\cdot 10^(-18)J)=9.12\cdot 10^(-8) m`