Calculate the energy (in kJ/mol) required to remove the electron in the ground state for each of the following one-electron species using the Bohr model.
(a) He+
kJ/mol
(b) Li2+
kJ/mol
To calculate the energy required to remove the electron in the ground state for each of the one-electron species using the Bohr model, you can use the formula:
E = - R_H / n^2
Where:
E is the energy of the electron in the hydrogen-like atom
R_H is the Rydberg constant for hydrogen (2.18 x 10^-18 J)
n is the principal quantum number (the energy level of the electron)
For (a) He+ (helium ion with 1 electron), the atomic number is 2, so the electron configuration is 1s^2. Since one electron is removed, the configuration becomes 1s^1.
Using the formula above, we can calculate the energy required to remove the electron:
E = - R_H / n^2
E = - (2.18 x 10^-18 J) / 1^2
E = - 2.18 x 10^-18 J
To convert the energy to kilojoules per mole, we can use the following conversion:
1 J = 1 kJ/1000 J
1 mole = N_A molecules
For (a) He+:
Energy (in kJ/mol) = (-2.18 x 10^-18 J) * (1 kJ/1000 J) * N_A
Where N_A is Avogadro's constant (6.022 x 10^23 mol^-1).
For (b) Li2+ (lithium ion with 1 electron), the atomic number is 3, so the electron configuration is 1s^2 2s^0. Since one electron is removed, the configuration becomes 1s^2.
Using the formula above, we can calculate the energy required to remove the electron:
E = - R_H / n^2
E = - (2.18 x 10^-18 J) / 1^2
E = - 2.18 x 10^-18 J
To convert the energy to kilojoules per mole, we can use the following conversion:
1 J = 1 kJ/1000 J
1 mole = N_A molecules
For (b) Li2+:
Energy (in kJ/mol) = (-2.18 x 10^-18 J) * (1 kJ/1000 J) * N_A
Please note that these calculations are based on the Bohr model, which is an oversimplified model and does not accurately describe the behavior of more complex atoms or ions.
See your post later. b is done the same way a is done.
Z = 2^2 for He^+
Z = 3^2 for Li^2+