When an electron makes a transition from its first quantum level to ground level, the energy difference is carried by the emitted photon. In comparison, how much energy is needed to return an electron at ground level to the first quantumlevel?
The energy required to restore the atom to the first quantum level is the same as that of the photon emitted in the reverse process.
To calculate the energy needed to move an electron from the ground state to the first excited state, you can use the formula:
ΔE = E_initial - E_final
where ΔE is the change in energy, E_initial is the energy of the ground state, and E_final is the energy of the first excited state.
The energy of an electron in a specific quantum level can be calculated using the formula:
E = -13.6 eV/n^2
where E is the energy, -13.6 eV is the ionization energy of a hydrogen atom, and n is the principal quantum number.
For the ground state (n = 1), the energy is:
E_initial = -13.6 eV/1^2 = -13.6 eV
For the first excited state (n = 2), the energy is:
E_final = -13.6 eV/2^2 = -13.6 eV/4 = -3.4 eV
Now we can calculate the energy difference:
ΔE = E_initial - E_final = -13.6 eV - (-3.4 eV) = -10.2 eV
Therefore, it would take approximately 10.2 electron volts (eV) of energy to move an electron from the ground state to the first excited state.