When an electron makes a transition from its first quantum level to the 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 quantum level?
The same amount of energy is required. It can come from photon absorption or collision
To calculate the energy required for an electron to transition from the ground level to the first quantum level, we need to understand the energy levels and transitions in an atom.
In an atom, electrons occupy specific energy levels or shells. The energy levels are quantized, meaning they exist at discrete energy values. The lowest energy level, closest to the nucleus, is called the ground state or ground level. The higher energy levels are referred to as excited states.
When an electron transitions from a higher energy level to a lower energy level, it releases energy in the form of a photon. The energy of the emitted photon is equal to the energy difference between the initial and final energy levels of the electron.
In this case, we are considering the transition of an electron from the first quantum level (excited state) to the ground level. The energy difference between these two levels corresponds to the energy of the photon emitted during the transition.
To determine the energy difference, we can use the formula:
ΔE = E_final - E_initial
Here, ΔE represents the energy difference, E_final is the energy of the ground state, and E_initial is the energy of the first quantum level.
For a hydrogen atom, the energy levels are given by the formula:
E = -13.6 eV/n^2
Where n is the principal quantum number.
To calculate the energy difference, let's first determine the energies of the ground state and the first quantum level:
For the ground state (n=1),
E_ground = -13.6 eV/1^2 = -13.6 eV
For the first quantum level (n=2),
E_first_quantum = -13.6 eV/2^2 = -13.6 eV/4 = -3.4 eV
Now let's calculate the energy difference:
ΔE = E_ground - E_first_quantum
= -13.6 eV - (-3.4 eV)
= -13.6 eV + 3.4 eV
= -10.2 eV
So, the energy difference between the ground state and the first quantum level is -10.2 eV.
To return the electron from the ground state to the first quantum level, energy equal to +10.2 electron volts (eV) would be needed.