In order to solve this question, we must apply the conservation of mass. The total number of nucleons (upper number) and protons (lower number) must be equal before and after the decay. The new nucleon number is
218 - 4
= 214
And new proton number is
84 - 2
= 82
Next, we must identify which element has the proton number 82. That would be lead, Pb.
Therefore, the answer is
5. ²¹⁴Pb₈₂
There are 5 valence electrons in a atom of phosphorus.
A circuit with many paths for the current to travel through and not simply one is classified as a parallel circuit. Here the circuit can have many loops of resistors or light bulbs that can be attached.
For this problem we can use half-life formula and radioactive decay formula.
Half-life formula,
t1/2 = ln 2 / λ
where, t1/2 is half-life and λ is radioactive decay constant.
t1/2 = 8.04 days
Hence,
8.04 days = ln 2 / λ
λ = ln 2 / 8.04 days
Radioactive decay law,
Nt = No e∧(-λt)
where, Nt is amount of compound at t time, No is amount of compound at t = 0 time, t is time taken to decay and λ is radioactive decay constant.
Nt = ?
No = 1.53 mg
λ = ln 2 / 8.04 days = 0.693 / 8.04 days
t = 13.0 days
By substituting,
Nt = 1.53 mg e∧((-0.693/8.04 days) x 13.0 days))
Nt = 0.4989 mg = 0.0.499 mg
Hence, mass of remaining sample after 13.0 days = 0.499 mg
The answer is "e"
