Work and Energy

Energy Level

Energy level refers to a fixed distance from an atom’s nucleus where electrons may exist. Furthermore, energy levels can be thought of like the steps of a staircase. Just like one can stand on one step or another but not in between the steps, electrons also can occupy one energy level or another but not the space that is present between energy levels.

Introduction to Energy Level

A quantum mechanical system or particle that is confined spatially—can only take on energy levels. Furthermore, an energy level is a certain discrete value of energy. This is in contrast to the classical particles that can possess any amount of energy.

The common use of the term ‘energy level’ is for the energy levels of the electrons in atoms, molecules, or ions whose bounding takes place by the nucleus’s electric field. Moreover, the term can also refer to energy levels of nuclei or rotational or vibrational energy levels of the molecules. Also, experts call the energy spectrum of a system characterized with such discrete energy levels as quantized.

energy level

                                                                                                                     Energy Level

Formula of Energy Level

When it comes to the energy level formula, one must look at the Bohr model of the hydrogen atom. In the Bohr model of the hydrogen atom, an assumption was made concerning the quantization of atoms. According to this assumption, the orbiting of the electrons takes place around the nucleus in specific orbits or shells that are characterized by a fixed radius.

Only those shells were allowed whose radius was provided by the equation given below. Moreover, it was not possible for electrons to be present between the shells. Mathematically, the expression of the equation for the allowed value of the atomic radius is as

r(n) = n2 × r(1)

Formula of Energy of Electron

Bohr made the calculation of the energy of an electron in the hydrogen’s atom nth level by considering the electrons in orbits that are circular and quantized. One can see this below in the form of energy of electron formula:

E(n) = \(-\frac{1}{n^{2}}\times 13.6Ev\)

where 13.6 eV is the hydrogen electron’s lowest possible energy.

An electron absorbs energy in the form of photons and consequently, its excitement takes place to a higher energy level. After jumping to the higher energy level, the excited state, the excited electron becomes less stable and quickly emits a photon to return to a more stable energy level.

The energy that is emitted is equivalent to the difference between the two energy levels for a specific transition. The calculation of this energy can take place by using the following equation

hv = ΔE = \(\left ( \frac{1}{n^{2}_{low}}-\frac{1}{n_{high}^{2}}\right )13.6Ev\)

The formula for defining the hydrogen atom’s energy levels is below

E = \(\frac{E_{0}}{n^{2}}\)

where E0 is 13.6 eV and n is 1,2,3……and so on

FAQs For Energy Level

Question 1: Explain the concept of energy level?

Answer 1: Quantized energy levels are the result of the relationship that exists between a particle’s energy and its wavelength. For a confined particle like an atom’s electron, the wave function will be characterized by a form of standing waves. Furthermore, it is possible only for stationary states to exist whose energies correspond to integral numbers of wavelengths.

As for the other states, the waves interfere destructively, thereby leading to a probability density that is zero. Furthermore, particle in a box and the quantum harmonic oscillator are some of the elementary examples that mathematically show the coming about of the energy levels.

Question 2: What is Bohr’s atomic model?

Answer 2: As for the questions about the energy of an atom and its stability, the atomic models of Thomson and Rutherford were unable to provide answers.  In the year 1913, Niels Bohr came up with an atomic model. Moreover, this model describes the atom as a small, positively charged nucleus and the electrons surrounding it.

According to the model, electrons travel in circular orbits around the positively charged nucleus. This is certainly similar to how the planets in the solar system move around the sun.

Furthermore, the electrostatic force provides the attraction. Most noteworthy, this model is Bohr’s atomic model.

Bohr’s model provides a proper explanation for the stability of electrons that revolve in orbits. Furthermore, the name that Bohr gave to these orbits is energy shells.

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