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 an electron in the ground state for each one-electron species using the Bohr model, we can use the following formula:
E = -13.6 / n^2
where E is the energy, n is the principal quantum number for the electron's energy level.
For the first case, He+:
(a) He+ has an atomic number of 2, which means it only has one electron. Since it has a positive charge (+1), it means that the electron has been removed once from the neutral helium atom.
Using the formula, we can substitute n = 1:
E = -13.6 / 1^2
E = -13.6 kJ/mol
Therefore, the energy required to remove an electron from He+ in the ground state is -13.6 kJ/mol.
Now, let's move on to the second case, Li2+:
(b) Li2+ has an atomic number of 3, which means it typically has three electrons. However, since it has a positive charge (+2), it means two electrons have been removed from the neutral lithium atom.
Using the formula, we can substitute n = 1:
E = -13.6 / 1^2
E = -13.6 kJ/mol
Therefore, the energy required to remove an electron from Li2+ in the ground state is -13.6 kJ/mol.
To calculate the energy required to remove an electron in the ground state using the Bohr model, we can use the formula:
E = -13.6 * (Z^2 / n^2) kJ/mol
where E is the energy required, Z is the atomic number of the species, and n is the principal quantum number of the electron.
Let's calculate the energy required for each of the one-electron species:
(a) He+:
In the case of He+, the atomic number Z is 2 (since it has one proton and one electron has been removed) and the electron is in the ground state, so n = 1.
E = -13.6 * (2^2 / 1^2) = -13.6 * 4 = -54.4 kJ/mol
Therefore, the energy required to remove an electron in the ground state for He+ is -54.4 kJ/mol.
(b) Li2+:
In the case of Li2+, the atomic number Z is 3 and the electron is in the ground state, so n = 1.
E = -13.6 * (3^2 / 1^2) = -13.6 * 9 = -122.4 kJ/mol
Therefore, the energy required to remove an electron in the ground state for Li2+ is -122.4 kJ/mol.
testing
For He^+,
E = 2.180E-18 J*Z^2(1/n2)
Z is the atomic number of He. n is the principal quantum number of the for the one remaining electron. This will give you J per photon. You need to multiply by 6.02E23 for J/mol then convert to kJ/mol.