Write a correct and complete nuclear equation for the alpha decay of a parent atom having 102 protons and 167 neutrons useing the symbols for the elements actually involved in the process?

Alpha partical is a He nucleus. When decaying alpha particle mass is reduced by 4 and atomic number is reduced by 2.

The actual element which has 102 protons is No (Nobelium). 
Since it has 167 neutrons, the mass = protons + neutrons = 102 + 167 = 269

after an alpha decay, the new element formed has 100 protons which is Fm ( Fermium)

the alpha decaying equation is,

    ₁₀₂²⁶⁹No → ₁₀₀²⁶⁵Fm + ₂⁴α + heat

the total mass and the atomic number( numbe rof protons) must be equal in both sides.

They are all decomposition reactions.