Hadissarren Hausa na Zuruwa Masu Karamin Elektironi Duniya

An kafuwa da suka yi wani abu mai mahimmanci da ya zama da sunan metallic bonding da suka biye da lattice structure. Abin da yake da mahimmanci a fannonin wannan irin haɗa shi ne cewa ba tare da ionic bonding ko covalent bonding inda sharhiyar electrons ke tsakanin biyu atoms kuma electrons suka baki da muhimmanci, a metallic bonding an yi haɗa daga duka atoms a lattice da free electrons daga har atomi an sharhiya ta hanyar duk lattice. Wannan free electrons sun yi lafiya daga baya zuwa baya a cikin lattice kuma saboda haka ana kiran su da electron gas.
Nufin electron-electron interaction da kuma electron-ion interaction, ya fi samu cewa electrons sun yi lafiya a cikin box mai kyau da suke sa ions a cikin lattice. Wannan fahimta ya bayar Drude da ya amfani da shi don bayyana al'adun metals daidai kamar electrical conductivity, thermal conductivity, etc.

Drude ya amfani da equations of simple mechanics hanyar electrons don tabbatar da duk expressions kuma tafi Ohm’s Law. Yanzu electrons suna yi lafiya a cikin lattice na musamman saboda thermal energy, kuma net average effect ya zama zero. Amma idan electric field ya zama da metal, wata abu mai gudummawa na velocity ya faruwar da ita saboda force da ya yi ita da sake ita.

A cikin Newtonian mechanics muna iya rubuta-

Idan, e= charge on electron,
E = applied electric field in V/m
m = mass of electron
x = distance in the direction of motion.

Integrating equation (i)

Idan, A and C are constants.

Equation (ii) ita ce equation of velocity of electrons, hence C has dimension of velocity, and can only be random velocity of electron which it had at the initial stage when no field was applied. Hence,
Amma, kamar yadda aka magana a baya wannan random velocity averages out to zero, thus the average velocity of the electrons can be written as-

Wannan equation ya nuna cewa velocity keeps on increasing indefinitely with time until E is switched on, however this is not possible. The explanation to this is given by saying that the electrons do not move freely in the lattice, rather they collide with the ions present in the lattice structure, and loose their velocity and again gets accelerated and again collides and so on.

Hence seeing the average effect we consider that on an average the time between two collisions is T, known as the relaxation time or collision time and the average velocity attained by electrons in T time period is known as drift velocity.

Now, for number of electrons per unit volume as n, the amount of charge passing through a cross section A in time dt will be given by

Hence the current flowing will be given by,

And hence the current density will be,

Putting the value of drift velocity from equations (iv) in (v),

Which is nothing but the Ohm’s Law itself, where,

Now here we define a new term known as mobility, defined as drift velocity per unit electric field,

Its unit is