# Question d7de9

Feb 16, 2015

The minimum frequency needed is $1.84 \cdot {10}^{15} \text{Hz}$.

The first thing you need to do is find out how much energy is required to ionize one magnesium atom. You do that by using Avogadro's number to go from moles to atoms

$738 \text{kJ"/"mol" * ("1 mole")/(6.022 * 10^(23)"atoms") = 1.22 * 10^(-21)"kJ/atom}$

The relationship between energy and frequency is described by the Planck-Einstein equation, or

$E = h \cdot \nu$, where

$E$ - energy;
$h$ - Planck's constant - $6.626 \cdot {10}^{- 34} \text{J" * "s}$;
$\nu$ - frequency;

Since Planck's constant uses Joules, convert the value you have for the ionization energy of one atom from kJ to J

$1.22 \cdot {10}^{- 21} \text{kJ" * ("1000 J")/("1 kJ") = 1.22 * 10^(-18) "J}$

Now just plug this value into the Planck-Einstein equation

E = h * nu => nu = E/h = (1.22 * 10^(-18) "J")/(6.626 * 10^(-34)"J" * "s"#

$\nu = 1.84 \cdot {10}^{15} {\text{s}}^{- 1}$, or $1.84 \cdot {10}^{15} \text{Hz}$