Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions 257

Analyzing the motion of the second ball, we
neglect the influence of the first released ball.
Then

q 2 1 1 1

2 4neo k a l^ (1^3 + • • '^ '

i.e. one of the nearest neighbours is missing in the

parentheses. Therefore,

mu 2 mill 0

K— i —

2 2 4neoa '

or

q= lI4neoKa.

3.18. According to the momentum conservation law,

mu (m M) u,

where m is the mass of the accelerated particle,

M is the mass of the atom, and u is their velocity

immediately after the collision.

We denote by W 10 „ the ionization energy and

write the energy conservation law in the form,

mu 2 , (m +M) u 2

2 = vv ion 2

Eliminating the velocity u from these equations,

we obtain

mui , m

(^2) = ( 1 -r —m.
If m is the electron mass, then m/ili < 1, and the
kinetic energy required for the ionization is
mu'
2
When an atom collides with an ion of mass
m x M, mv 2 /2 x 2Wion, i.e. the energy of the
ion required for the ionization must be twice as
high as the energy of the electron.
Wion•
17-0771