Introduction
Metal crystallizes with cubic close packed structure, and the sin2 value of brag reflection of Miler planes (200) and (111) are given as 0.18 and 0.14, respectively. The objective is to determine the unit length of the metal.

Explanation
The sin2 value of brag reflection is given by the formula:

sin2θ = λ^2/(4a^2)

Where sin2θ is the sin2 value of brag reflection, λ is the wavelength of X-rays used, and a is the unit length of the crystal.

Using the given sin2 values and assuming the same wavelength of X-rays used for both Miler planes, we can express the equation as:

0.18 = λ^2/(4a^2) for (200) Miler plane
0.14 = λ^2/(4a^2) for (111) Miler plane

Solving for a in both equations, we get:

a = λ/√(4sin2θ)

Substituting the values for sin2θ and assuming a common wavelength of X-rays used, we get:

a = λ/√(4(0.18)) for (200) Miler plane
a = λ/√(4(0.14)) for (111) Miler plane

Simplifying the equations, we get:

a = 0.290λ for (200) Miler plane
a = 0.335λ for (111) Miler plane

Therefore, the unit length of the metal is dependent on the wavelength of the X-rays used. The specific value of the unit length cannot be determined without knowing the wavelength of the X-rays used.

Conclusion
Metal crystallizes with cubic close packed structure. The sin2 value of brag reflection of Miler planes (200) and (111) are given as 0.18 and 0.14, respectively. The unit length of the metal is dependent on the wavelength of the X-rays used, and cannot be determined without knowing the wavelength of the X-rays used.