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Physics Topics can be challenging to grasp, but the rewards for understanding them are immense.
What is the Value of 1 eV?
Quantum theory or quantum physics is the mainstay of modern physics. This theory is primarily applicable to microscopic world, i.e., physics of atomic domain. The study of this branch started almost at the beginning of the twentieth century. In quantum theory, we come across those phenomena or facts which are beyond our common experience and are apparently non-realistic. Scientists who established the main foundation of this theory were also surprised to see the inferences obtained from theoretical analysis of the theory. But all experiments conducted so far have strengthened the base of the theory.
Quantised quantity and quantum: Some quantities, obtained in daily life, can have only chosen values. These values are obtained, generally, by multiplying a primary value by an integer. Such quantities are called quantised quantities and the primary value is called a quantum of the respective quantity. As for example, currency is quantised and previously, in Indian currency, 1 paisa was its quantum. It was possible to pay 1 rupee 6 paise or 106 paise but payment of 106.5 paise was not possible.
Scientist Max Planck propounded his quantum theory in 1900 AD. In spite of astounding success of wave theory of light, this theory cannot explain phenomena like black body radiations, photoelectric effect, atomic spectra, etc. Basically, to explain black body radiation spectrum, Max Planck introduced quantum theory. Later, concept of photon particles, introduced by Einstein, established the theory more firmly.
Properties of an electron:
Charge: Electron is negatively charged. The magnitude of charge of an electron is,
e = 1.6 × 10-19C in SI
= 4.8 × 10-10 esu of charge in CGS system
From different experiments, we learnt that, charge of a body is a quantized quantity and quantum of charge is the charge of an electron (e). So, values of charges can be +2e, -5e, 1000e, etc. but values like 1.5e, -2.8e are non-realistic.
Rest mass: Rest máss of an electron,
m0 = 9.1 × 10-31 kg = 9.1 × 10-28g
If speed of an electron is much less than the speed of light, there is no difference between its rest mass (m0) and effective mass (m). Thus mass of electron, m = m0.
Kinetic energy of an electron, electronvolt: Velocity of electron increases on being attracted by a positive potential and hence its kinetic energy also increases. On the other hand, when repelled by a negative potential, velocity of electron decreases. Kinetic energy of an electron is usually expressed in electronvolt (eV) unit.
Definition: The change in kinetic energy of an unbound electron, as it travels across a potential difference of 1V, is called 1 eV.
1 eV = charge of an electron × 1V
= 1.6 × 10-19C × 1V = 1.6 × 10-19J [∵ C ᐧ V = J]
= 1.6 × 10-19 × 107 erg = 1.6 × 10-12 erg
Electronvolt is a very small unit compared to erg or joule. Hence, it is mainly used in nuclear or atomic physics only.
1 keV = 103eV; 1MeV = 106eV
Quarks: The discovery of quarks by Gell-Mann in 1964 has destroyed the myth that nucleons (protons and neutrons) are the fundamental particles of matter which are incapable of further division, and that the charge on the electron was the smallest possible charge existing in nature. Quarks have been identified as the fundamental charged particles constituting baryons and mesons. So far, six quarks with their corresponding antiquarks (\(\bar{u}\) \(\bar{d}\) \(\bar{c}\) \(\bar{s}\) \(\bar{t}\) \(\bar{b}\) have been detected : up (u), down (d), charm (c), strange(s), top (t), bottom (b), with electric charge +\(\frac{2}{3}\)e, and –\(\frac{1}{3}\)e [to be taken alternately in that order], e being the electronic charge.
Thus, for example, proton is composed of u, u, d, while neutron is composed of u, d, d, held by mediator particles called gluons. Mesons are composed of quark-antiquark pairs. Incidentally, in the current view, all matter consists of three kinds of particles: leptons, quarks and mediators, (details are beyond the scope of the present discussion).
Numerical Examples
Example 1.
What is the energy of a photoelectron, in electronvolt, moving with a velocity of 2 × 107 m ᐧ s-1? (Given, mass of electron = 9.1 × 10-28g)
Solution:
Mass of electron = 9.1 × 10-28 g = 9.1 × 10-31 kg
Kinetic energy of the electron
= \(\frac{1}{2}\)mv2 = \(\frac{1}{2}\) × (9.1 × -31) × (2 × 107)2J
= \(\frac{1}{2}\) × {\(\frac{9.1 \times 10^{-31} \times\left(2 \times 10^7\right)^2}{1.6 \times 10^{-19}}\)}eV = 1137.5 eV