D. Using a fixed-pulley system
To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as

As M=m, then

Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then



Therefore replacing we have that,

Re-arrange to find v,



Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that

Therefore




Therefore the velocity when they are about to collide is 
<em>An is formed when an atom loses or gains one or more electrons. Because the number of electrons in an ion is different from the number of protons, an ion does have an overall electric charge. Consider how a positive ion can form from an atom. The left side of the illustration below represents a sodium (Na) atom</em>
Answer:

Explanation:
Give that,
The potential difference of the electrons, 
We need to find the wavelength of the electrons.
Using the conservation of energy,

Put all the values,

So, the wavelength of the electrons is
.