Acceleration obtained by ions ay = fym0...②
How long do ions move between plates? t0=Lv0…③
When it reaches the right edge of the electrode plate, the partial velocity of ions in the +y direction vy=ayt0…④.
Time required for ions to reach the screen from the right end of the flat panel t' 0 = dv0...⑤
How far is the ion from the O point when it hits the screen? y0= 12ayt20+vyt'0
From the above, get? y0=q0EL(L+2D)2mv20? …⑥
(2) Let the ion charge amount be q, the mass be m, the incident velocity be v, the magnetic induction intensity of the magnetic field be b, and the Lorentz force of the magnetic field on the ion Fx=qvB…⑦.
It is known that the incident velocity of ions is very high, so the time for particles to move in the magnetic field is very short.
Compared with a circle, the arc it passes through is very small. When moving in the plate, the component velocity of OO' is always much higher than that of X and Y directions, and the Lorentz force changes little, so it can be treated as a constant force. The acceleration ax generated by Lorentz force is equal to qvbm...⑧
Ax is the acceleration of ions in the x direction, and the movement of ions in the x direction can be regarded as a uniformly accelerated linear motion with zero initial velocity. When it reaches the right end of the electrode plate, the fractional velocity of ions in the X direction VX = AXT = QVBM (LV) = QBLM … 9.
When ions fly out of the polar plate and reach the screen, the distance from point O in the X direction is x = vxt ′ = qBLM (DV) = qldmv … attending.
When the initial velocity of ions is arbitrary, the position of ions when they reach the screen deviates from O point Y in Y direction. Consider formula ⑥, y = qeldmv2...( 1 1).
X2 = kmy...( 1 1) from two formulas.
Where k = qb2lde
The above formula shows that k is a constant value independent of the initial velocity of ions entering the plate, which is the same for both ions.
According to the conditions, a light spot with x coordinate of 3.24mm corresponds to carbon ion 12, and its mass is m 1= 12u, while a light spot with x coordinate of 3.00mm corresponds to unknown ion.
Let its mass be m2, and if the formula (12) is substituted into the data, we can get m2 ≈ 14u...( 13).
So the mass number of the unknown ion is 14.