Question

An energy of 13.6 eV is needed to ionize an electron from the ground state of a hydrogen atom. Selecting the longest wavelength that will work from the those given below, what wavelength is needed if a photon accomplishes this task

Answer 1

The wavelength is
`\lambda = 91nm`

Step-by-step explanation:

From the question we are told that

The energy required is
`E = 13.6 \ eV`

This energy needed in form of a photon can be mathematically represented as

`E = (h * c )/(\lambda )`

where h is the Planck constant with a value
`h = 4.1357 * 10{-15} eV \cdot sec`

and c is the speed of light which is

substituting values

`13.6 eV = ( 4.1357 * 10^(-15) eV * 3.0*10^8 )/(\lambda )`

= >
`\lambda = 9.1*10^(-8)`

`\lambda = 91nm`