Final answer:
The formula ΔE = hν describes the change in energy of electrons when they transition between energy levels, incorporating Planck's constant and the frequency of the emitted photon.
Step-by-step explanation:
The formula used to describe the change in energy of electrons jumping from higher energy levels to lower energy levels is ΔE = hν. This formula indicates that the energy change (ΔE) is equal to Planck's constant (h) multiplied by the frequency of the photon emitted (v). It's important to note that energies of bound electrons are quantized and the energy levels are given by En = -13.6 eV / n², where 13.6 eV is the energy necessary to ionize the hydrogen atom, and n represents the principal quantum number of the electron's orbit. The energy of the photon that is emitted when an electron transitions from a higher orbit 'n' to a lower orbit is given by the difference in these energy levels (E1 - Ef).
This formula is part of the Bohr model of the atom, where ΔE represents the change in energy, -13.6 eV is a constant related to the energy levels in hydrogen atoms, and n is the principal quantum number representing the energy level of the electron. The negative sign indicates that the energy is released as the electron transitions to a lower energy level.
The other options are:
a. E=mc^2 - This formula relates energy (E) to mass (m) and the speed of light (c), and is associated with mass-energy equivalence in the theory of relativity.
b. ΔE = hν - This formula is related to the energy of a photon, where ΔE is the change in energy, h is Planck's constant, and ν is the frequency of the photon.
d. ΔE = mv - This formula represents the kinetic energy of an object with mass (m) and velocity (v), but it is not specifically related to electron energy levels in an atom.