- Computer programm
- experiment simulationIn the year 1896 John Thomson investigated cathode rays and discovered electron - the first elementary particle. In 1911, in the similar way, he tried to study atomic nucleus. He obtained a beam of positive ions inserting gas into a vessel. There were two electrodes in the vessel. Between them there occurred magnetic field dislocating electrons (picture no. 1).
The electrons were moving to the positive charged anode, and the positive ions were moving to the cathode. In the cathode there was a channel leading ions out of the instrument. The ions ran then between the charged electrodes D and E. Between them there was the electric field with intensity E. And the ions were running also between magnet's poles S and N. The intensity of those poles was equal B. The ions beam was abberated both by the electric field (vertically) and by the magnetic field (horizontally). The force from the first field equals:
(1)
From the second Newton's law:
(2)
where m - electron mass, a - molecule acceleration The particle in the field moved along the path trajectory which was the circular arc; the circle radius was equal r. So the occurring acceleration was the acceleration of the circular motion:
(3)
After connecting formulas (1), (2) and (3):
(4)
Iv of every ion is the same and there is only the electric field on then the beam will hit the screen at the point 1.
The force of the magnetic field, directed perpendicular to the field's direction and to ions' velocity, abberating the path trajectory of the beam (which becomes the circular arc with the circle radius r1) is equal:
(5)
After connecting that formula, the second Newton's law and the formula of the centripetal acceleration of the circular motion:
(6)
If v of all ions are the same and there is only the magnetic field switched on then the beam will hit the point 2.
And if the both fields are switched on then every ion will be influenced by both forces and by the constant v the beam will hit the point 3. The beam leaves the track on the screen which is the photographic plate. But the v of different ions is different so, on the screen there is not a single point but the sign of parabola. If all ions have the same mass and the charge then there is only one sign of parabola on the screen.
But investigating neon, Thomson got two parabolas because of two atomic masses of the element (equal 20 and 22). Isotopes were discovered.
In 1919 Francis William Aston found different, more exact way to measure the content of isotopes in the total amount of the element. He constructed an instrument called mass spectrograp. The instrument consisted from ions source (working similar to the Thomson' one), two narrow slice (Sz1 and Sz2), two parallel plates P1 and P2 (between them, by impressing voltage, there creates the electric field), beam stop, permanent magnet, screen and photographic plate (picture no. 2).
Ions from the source, after going through slice, create a narrow beam which next is diffused by the electric force (the yaw angle of ions is inversely proportional to their kinetic energy thanks to what the separation of the ions of different velocities is possible). Than, the beam of ions goes through the magnetic field so, ions trajectories are abberated to the other side. The magnetic field abberates the ions trajectory by the angle which is directly proportional to particles momentum. Ions go through that two fields with the same q/m (the charge to mass proportion). Thanks to it they can agglomerate in the one point of the photographic plate. By analysing the dark points of the plate (where ions hit) its possible to investigate isotopes. Different in mass hit different in places on the plate. The blackening of the points is proportional to the number of hitting points. The spectrograph, made in 1919 and working until 1925, let evaluate the atomic mass of isotopes with the accuracy to 1 percent. That accuracy was not enough because the differences of many isotopes masses to the total masses were also of order of 1 percent.
Not a long time later another scientist - Arthur Jeffrey Dempster constructed more developed instrument. The ions source was the incandescent spiral with metal evaporating. Leaving the spiral ions had very small velocity. Then they were accelerated by the electric field. It let to get a beam of ions of almost identical energies. To separate the ions with different masses the magnetic field was enough. The instrument let the precision of measurements be 100 times multiplied.
I n the 30-ties K. T. Bainbridge constructed the spectrograph with double focal distance of the ions beam. The measurements were even more exact. The beam went through the space where the magnetic and the electric field were crossed. According to the formula (1) there is a upward force influencing in the electric field. And according to the formula (5) there is a downward force influencing the ions in the magnetic field. He constructed the instrument this way not to let other ions then the ones with the not curved trajectory move out the space of fields. That were the ones on which the magnetic and the electric force equilibrate:
(7)
So the velocity of ions moving farther equals:
(8)
There is a force influencing the charged molecules moving with the similar velocity v. The velocity is directed perpendicularly to the line of magnetic field (the vector of induction B) created by the permanent magnet. The force is perpendicularly to the vector of velocity v and to the vector B. The particle moves by the circle. The force given by formula (5) is the centripetal force: :
(9)
where m - particle's mass, so:
(10)
Until 1937 Aston evaluated the quantity of atomic mass of different isotopes. The accuracy of atomic mass of different isotopes. The accuracy of his measurements were of the order of the 5-th place after the decimal point.
The discovery of isotopes gave the answer for the question of not total masses of atoms. Almost a hundred years before William Prout brought forward a hypothesis that all atoms consisted of basal elements which mass is equal to hydrogen mass. But chlorine ruined the hypothesis because hi mass was equal about 35,5 masses of hydrogen. Now it was proved that there is no chlorine with mass equal 35,5 but two isotopes of chlorine with masses equal 35 and 37 in the proportions making the mean mass equal 35,46.
All the beginning of the 20th century scientist were of the opinion that atomic nucleus consisted of protons but also of some other component. That thesis was proved by the discovery of isotopes - atom of the same atomic number (the number of protons and electrons) but of different mass number.
In 1932 James Chadwick gave final, experimental proofs for the subsistence of the neutrons - neutral particles of nucleus, their mass is similar to proton's mass. The subsistence of neutron in the nucleus explained the fact of isotope's subsistence.
