NaOH reacts with CH3COOH in 1:1 molar ratio to produce CH3COONa
NaOH + CH3COOH → CH3COONa + H2O
Mol CH3COOH in 52.0mL of 0.35M solution = 52.0/1000*0.35 = 0.0182 mol CH3COOH
Mol NaOH in 19.0mL of 0.40M solution = 19.0/1000*0.40 = 0.0076 mol NaOH
These will react to produce 0.0076 mol CH3COONa and there will be 0.0182 - 0.0076 = 0.0106 mol CH3COOH remaining in solution unreacted . Total volume of solution = 52.0+19.0 = 71mL or 0.071L
Molarity of CH3COOH = 0.0106/0.071 = 0.1493M
CH3COONa = 0.0076 / 0.071 = 0.1070M
pKa acetic acid = - log Ka = -log 1.8*10^-5 = 4.74.
pH using Henderson - Hasselbalch equation:
pH = pKa + log ([salt]/[acid])
pH = 4.74 + log ( 0.1070/0.1493)
pH = 4.74 + log 0.717
pH = 4.74 + (-0.14)
pH = 4.60.
Half life is the time taken by a radioactive isotope to decay by half its original mass. In this case, the halflife of the radioactive isotope is 5000 years.
Initially the mass is 100 %; thus the mass that will be left will be given by;
New mass = Original mass × (1/2)^n where n is the number of half lives;
n = 10000/5000 = 2
New mass = 100% ×(1/2)^2
= 100 % × 1/4
= 25%
Therefore; the mass left after 10000 years is 25% or 1/4 of the original mass.
Answer to this is Radioactive isotopes.
Isotopes are the species of the same element having different atomic masses that means the number of protons remains the same but number of neutrons do differ. For example
and
are the two isotopes of Hydrogen (
).
Radioactive isotopes are the isotopes which release some kind of energy in the form of alpha particles, beta particles or gamma radiation. Examples of each of the decay processes are :
Alpha Decay: In this decay one alpha particle having atomic mass 4 and atomic number 2 or we can say a He molecule will come out. 
Beta Decay: In this decay a
particle is emitted increasing the atomic number of the reactant by 1 unit.

Gamma Radiation: In this type of reaction only radiation is emitted out which does not change the original molecule.

Evaporating is the right one