# The work function of an element is the energy required to remove an electron from the surface of the solid. Th

The work function of an element is the energy required to remove an electron from the surface of the solid. The work function for lithium is 279.7 kJ/mol (that is, it takes 279.7 kJ of energy to remove one mole of electrons from one mole of Li atoms on the surface of Li metal). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal?

1.) mn?

• The energy (E) contained within a single photon of light with frequency, v, is given by,

E = hv

Where h is Planck’s constant.

h = 6.63 E-34 J s

We are given that the work function to remove the first electron from Lithium metal is 279.7 kJ/mol.

Let’s convert this into an energy value per atom since the photon can only be absorbed by 1 electron around a single atom.

1 mole of atoms = 6.022 E23 atoms.

1 kJ = 1000 Joules

So we can convert the work function to be,

w = 279700 Joules / 6.022 E23 atoms

w = 4.645 E-19 Joules per atom

This is the minimum energy of the photon striking the electron around the Lithium atom which is capable of completely removing the electron.

Now if we take this minimum energy value and plug it into our equation above about the energy of a photon with a given frequency we will get,

4.645 E-19 J = (6.63 E-34 J s) * v

so we can solve for the frequency v to be,

v = (4.645 E-19 J) / (6.63 E-34 J s)

v = 7.01 E14 Hz would be the minimum frequency

We jjust solved for the minimum frequency of the light needed…but the question asked us for the maximum wavelength.

Frequency and wavelength are inversely proportional to each other. if we know the maximum of one of them we can find the minimum of the other.

Wavelength = c / v

Where c is the speed of light in vacuum (3 E8 m/s).

Wavelength = (3 E8 m/s) / (7.01 E14 Hz)

Wavelength = 4.28 E-7 meters

So the maximum wavelength of the light needed to strike a Lithium atom to remove its first electron is 428.2 nanometers.

EDIT:

Upon further research, I found that this question is wrong in its value for the first ionization energy of Lithium.

The first ionization energy of Lithium is about 520.2 kJ per mol, or about 5.392 eV per photon.

So although according the numbers provided in the question my answer is correct, don’t expect to actually ionize Lithium metal with 428.2 nm light…it would actually take a higher frequency (lower wavelength) light to do it. It would be around 1.3 E15 Hz or 230 nm.

http://education.jlab.org/itselemental/ele003.html

• definitely krypton. To make a noble gas, unstable by removing electrons requires huge amounts of engery… while potassium easily loses electrons due to its instability.

• Kj J Hv