Part a
Answer: 
For the arrangement considered in part a, all the atoms are aligned side by side along the side of the square surface.
Along one side of the square, the number of atoms that could fit 
This is along one side. On the entire surface:
Number of atoms 
Part b
Answer: 
consider the attached figure below:
The next layer of atoms are filled in the depressions of the first layer. The vertical distance between the two atoms would change. Consider an equilateral triangle drawn by joining the centers of the three atoms.
The atoms along the horizontal side would be aligned side by side; same as above 
The number of atoms along vertical side would vary. vertical distance between two atoms can be calculate using equilateral triangle as shown below.
an equilateral triangle has all the angles 
Let the vertical distance be y.
Then, 
where r is the radius of each atom. 
The number of atoms along the vertical side 
Total number of atoms in this kind of arrangement 
Answer:
a. 86.80 m
b. i. The mass of the bob
ii. The length of the pendulum
Explanation:
a. Determine the height of the smokestack.
Using T = 2π√(L/g) where T = period of pendulum = 18.7 s, L = length of pendulum = height of smokestack and g = acceleration due to gravity = 9.8 m/s².
So, making L subject of the formula, we have
T = 2π√(L/g)
T/2π = √(L/g)
squaring both sides, we have
(T/2π)² = L/g
L = (T/2π)²g
Substituting the values of the variables into the equation, we have
L = (T/2π)²g
L = (18.7 s/2π)²(9.8 m/s²)
L = (2.976 s)²(9.8 m/s²)
L = 8.857 s² × 9.8 m/s²
L = 86.796 m
L ≅ 86.80 m
b. What factors influence the period of a simple pendulum
The factors that influence the period of a simple pendulum are
i. The mass of the bob
ii. The length of the pendulum
To solve this problem it is necessary to apply the concepts related to Current and Load.
The current in terms of the charge of an electron can be expressed as
Where,
q = Charge
t = time
At the same time the Charge is the amount of electrons multiplied by the amount of these, that is
q = ne
Replacing in the first equation we have to
Clearing n,
Here the time is one second then
Therefore the number of electrons per second are passing any cross sectional area of the wire are 
The kinetic energy K = 0.5 * m * v² must be equal to the potential energy U = m * g * h.
m mass
v velocity
h height
g = 9.81m/s²
The mass m cancels out:
0.5 * v² = g * h
Solve for height h and transform to distance traveled.
(sin (4°) = height / distance)
It can solidify, it depends on the tempeture.
