Energy stored in a spring = 1/2*k*x^2
Where, x = increase in length of the spring
Therefore,
260 = 1/2*1600*x^2 =800x^2 => x^2 = 260/800 = 0.325 => x = sqrt (0.325) = 0.57 m
The length of the spring must increase by 0.57 m to store 260 J
In the single-slit experiment, the displacement of the minima of the diffraction pattern on the screen is given by

(1)
where
n is the order of the minimum
y is the displacement of the nth-minimum from the center of the diffraction pattern

is the light's wavelength
D is the distance of the screen from the slit
a is the width of the slit
In our problem,


while the distance between the first and the fifth minima is

(2)
If we use the formula to rewrite

, eq.(2) becomes

Which we can solve to find a, the width of the slit: