An X-ray photon of wavelength 0.954 nm strikes a surface. The emitted electron has a kinetic energy of 935 eV.

What is the binding energy of the electron in kJ/mol?

[KE =1/2 mv^2; 1 electron volt (eV) = 1.602 x 10^- 19 J]

u teach better than my chem professor

Well, isn't it electrifying to talk about binding energy! Now, let's crunch some numbers and have a blast.

First, let's convert the kinetic energy from eV to joules. We know that 1 eV is equal to 1.602 x 10^- 19 J, so we can calculate it as follows:

Kinetic Energy (J) = 935 eV * (1.602 x 10^-19 J/eV)

Now, let's find the number of electrons in 1 mol. I hope you're ready for some mind-boggling numbers because Avogadro's constant is coming!

The number of electrons in 1 mol = 6.022 x 10^23 electrons/mol

Finally, to find the binding energy in kJ/mol, we can use the formula:

Binding Energy (kJ/mol) = (Kinetic Energy (J) * 6.022 x 10^23 electrons/mol) / 1000

So, let me get my calculator ready to perform the calculations for you. Drumroll please...

To find the binding energy of the electron in kJ/mol, we can follow these steps:

1. Calculate the velocity of the emitted electron using the equation KE = 1/2 mv².

Given:
Kinetic energy (KE) = 935 eV
Mass of an electron (m) = 9.10938356 x 10^-31 kg (From the periodic table, we assume it's a single electron)

Since 1 electron volt (eV) = 1.602 x 10^-19 J, we can convert the kinetic energy to joules:

KE (J) = (935 eV) * (1.602 x 10^-19 J/eV)

2. Convert the wavelength of the X-ray photon from nm to meters:

Wavelength (m) = (0.954 nm) * (1 m / 10^9 nm)

3. Use the equation for the kinetic energy of a photon:

KE (J) = h * c / λ

Where:
h = Planck's constant = 6.62607015 x 10^-34 J·s
c = speed of light = 2.998 x 10^8 m/s
λ = wavelength of the photon (m)

Rearrange the equation to solve for λ:

λ = h * c / KE

4. Substitute the given values into the equation:

λ = (6.62607015 x 10^-34 J·s * 2.998 x 10^8 m/s) / KE

5. Calculate the binding energy per electron:

Binding energy per electron (J) = 1 / 2 mv^2

Note: This is the same as the kinetic energy of the emitted electron.

6. Calculate the binding energy per mole of electrons:

Binding energy per mole (J/mol) = Binding energy per electron (J) * Avogadro's number

Where:
Avogadro's number = 6.022 x 10^23 mol^-1

7. Convert the binding energy from joules to kilojoules:

Binding energy per mole (kJ/mol) = Binding energy per mole (J/mol) / 1000

Now we can substitute the values into the equations to find the binding energy per mole of electrons in kJ/mol.

To find the binding energy of the electron in kJ/mol, we need to convert the given kinetic energy from eV to joules and then calculate the number of joules per mole.

First, let's convert the given kinetic energy from eV to joules. We know that 1 electron volt (eV) is equivalent to 1.602 x 10^-19 joules.

Given kinetic energy: 935 eV

First, convert the eV to joules:
935 eV x (1.602 x 10^-19 J/eV) = 1.49652 x 10^-16 J

Now that we have the energy in joules, we can calculate the binding energy per electron. However, it is important to note that the binding energy per electron is directly related to the number of electrons involved in the reaction.

To calculate the binding energy per mole, we need to know the Avogadro's number, which is the number of particles (atoms, molecules, or electrons) in one mole of a substance. Avogadro's number is approximately 6.022 x 10^23 particles/mol.

Now, let's calculate the binding energy per electron:
Binding energy per electron = 1.49652 x 10^-16 J

To find the binding energy per mole, we need to multiply the binding energy per electron by Avogadro's number:

Binding energy per mole = Binding energy per electron x Avogadro's number
Binding energy per mole = (1.49652 x 10^-16 J) x (6.022 x 10^23 particles/mol)

Now, let's calculate the binding energy per mole:

Binding energy per mole = 9.00803 J/mol

Finally, let's convert the binding energy per mole from joules to kilojoules (kJ):

Binding energy per mole = 9.00803 J/mol x (1 kJ/1000 J)
Binding energy per mole = 0.00900803 kJ/mol

Therefore, the binding energy of the electron in kJ/mol is approximately 0.009 kJ/mol.

Energy of photon:

E = hc/λ
h = Planck’s constant = 6.626•10⁻³⁴ J•s = 4.14•10⁻¹⁵ eV•s
c = speed of light = 3•10⁸ m/s
λ = wavelength = 0.954 nm = 0.954•10⁻⁹m

E = 4.14•10⁻¹⁵•3•10⁸ / 0.954•10⁻⁹ =
=1302 eV

Binding energy is the difference between the energy of the photon and the kinetic energy of the electron:
E(b)= E(ph) – E(e) = 1302 - 935 = 367 eV
1 eV = 1.6•10⁻¹⁹J
367 eV = 5.87•10⁻¹⁷ J
The answer above is per electron, so for a mole of electrons, you multiply by Avogadro's number, 6.022•10²³ moles⁻¹.
5.87•10⁻¹⁷•6.022•10²³=3.536•10⁷J/mol=3.536•10⁴ kJ/mol