Explanation:
Given that,
Wavelength of the light, 
(a) Slit width, 
The angle that locates the first dark fringe is given by :



(b) Slit width, 
The angle that locates the first dark fringe is given by :



Hence, this is the required solution.
Answer:
particle's potential energy = 70J
Explanation:
From conservation of energy; K1 + Ue1 = K2 + Ue2
where K1 and K2 are the kinetic energies at two positions and Ue1 and Uue2 are the electrical potential energies at two positions.
k1 = 10J, Ue1 = 100J
K2 = 40J
substitute into K1 + Ue1 = K2 + Ue2
Ue2 = K1 + Ue1 - K2
= 10 +100 - 40
Ue2 = 70J