3. Using Bohr’s model of the atom, calculate the energy required to move an electron from a ground state
of n = 2 to an excited state of n = 3. Express your answer in both J/photon and kJ/mol.
E = 2.18E18 x (1/4 - 1/9) = ?J/photon.
?J/photon x 6.02E23 = J/mol. Change that to kJ/mol.
To calculate the energy required to move an electron from one energy level to another using Bohr's model, we can use the formula:
ΔE = -R_H(1/n_f^2 - 1/n_i^2)
Where:
ΔE is the change in energy
R_H is the Rydberg constant (2.18 × 10^-18 J)
n_f is the final energy level
n_i is the initial energy level
Given that the initial energy level is n_i = 2 and the final energy level is n_f = 3, we can substitute these values into the formula:
ΔE = -R_H(1/3^2 - 1/2^2)
Simplifying the equation:
ΔE = -R_H(1/9 - 1/4)
ΔE = -R_H(4/36 - 9/36)
ΔE = -R_H(-5/36)
Now we can calculate the value of ΔE:
ΔE = (2.18 × 10^-18 J)(5/36)
ΔE ≈ 3.0256 × 10^-19 J
To express the answer in kJ/mol, we need to convert the energy from Joules to kilojoules (1 kJ = 1000 J) and multiply by Avogadro's constant (6.022 × 10^23 mol^-1) as follows:
ΔE_kJ/mol = (3.0256 × 10^-19 J) × (1 kJ/1000 J) × (6.022 × 10^23 mol^-1)
ΔE_kJ/mol ≈ 1.82 kJ/mol
Therefore, the energy required to move an electron from the n = 2 to n = 3 energy level in Bohr's model is approximately 3.0256 × 10^-19 J/photon and 1.82 kJ/mol.