Use a proportion or dimensional analysis to determine the amount of energy (in kJ) needed to ionize 7.5 mol of sodium (Na(g) + 496 kJ →Na+(g) + e–).

1.24

⋅

10

15

Hz

Explanation:

Your strategy here will be to

use Avogadro's number to find the energy needed to ionize one atom of sodium

use the Planck - Einstein equation to find the frequency of light that corresponds to that specific energy

So, you know that the energy needed to ionize sodium is equal to

496 kJ/mol

. As you know, one mole of any element contains exactly

6.022

⋅

10

23

atoms of that element - this is known as Avogadro's number.

In your case, the energy needed to ionize one atom of sodium will be equal to

496

kJ

mol

⋅

10

3

J

1

kJ

⋅

1

mol

6.022

⋅

10

23

atoms

=

8.236

⋅

10

−

19

J/atom

The relationship that exists between energy and frequency is described by the Planck - Einstein equation

E

=

h

⋅

ν

, where

E

- the energy of the wave

h

- Planck's constant, equal to

6.626

⋅

10

−

34

J s

ν

- the frequency of the wave

Plug in your values and solve for

ν

, the frequency of light needed to ionize a sodium atom

Explanation:

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