The half life of a certain radioactive element is 800 years. how old is an object if only 12.5% of the radioactive atoms in it remains?

Given,  half life of a certain radioactive element = 800 years.

Amount of substance remaining at time t = 12.5%

Lets consider the initial amount of the radioactive substance  = 100%

Using the half life equation:

A = A₀(1/2)^t/t₁/₂

where A₀ is the amount of radioactive substance at time zero and A is the amount of radioactive substance at time t, and t₁/₂ is the half-life of the radioactive substance.

Plugging the given data into the half life equation we have,

12.5 = 100 . (1/2)^t/800

12.5/100 = (1/2)^t/800

0.125 = (0.5)^t/800

(0.5)^3 = (0.5)^t/800

3 = t/800

t = 2400 years

Thus the object is 2400 years  old.

explanation:

let the different atoms be x and y. each with four protons and same mass will be represented as follows.

mass number is number of protons + number of neutrons.

            and  

since, it is given that one has a negative charge while the other is neutral. therefore, there will be increase in number of protons and the atom will be represented as follows.

according to periodic table, mass number of beryllium is 9 and it has atomic number 4 so, the atoms will be and .  

the protons and neutrons will be located inside the nucleus whereas the electrons will be revolving around the nucleus.  

can you list the answers so i can answer