Question

The 99% of a radioactive element will decay between
A. 6 and 7 half lives
B. 7 and 8 half lives
C. 8 and 9 half lives
D. 9 half lives

Answer 1

Hint:Find the ratio between portion of radioactive element which is remaining or undecayed with 100, and use it in equation \[\dfrac{N}{{{N_0}}} = {\left( {\dfrac{1}{2}} \right)^n}\]to find n.

Formula used:
\[\dfrac{N}{{{N_0}}} = {\left( {\dfrac{1}{2}} \right)^n}\]
Here, N = Number of atoms undecayed after time t, \[{N_0} = \]Initial number of atoms present and n = Half life.

Complete step by step solution:
Radioactive decay is a spontaneous process by which an unstable nucleus loses energy in the form of radiation and the time duration in which the radioactive nuclei decay to half of its initial value is called its Half-life.

Given here is a radioactive element of which 99% is supposed to decay. Then the remaining percentage of the element which does not decay will be,
N= 1%
If \[{N_0} = 100\% \] is the initial percentage of element then,
\[\dfrac{N}{{{N_0}}} = \dfrac{1}{{100}} \\ \]
As we know that,
\[\dfrac{N}{{{N_0}}} = {\left( {\dfrac{1}{2}} \right)^n} \]
Where, n = Half life.
Therefore,
\[\dfrac{1}{{100}} = {\left( {\dfrac{1}{2}} \right)^n} \\
\Rightarrow {2^n} = 100\]
Here, n will lie between 6 and 7. Hence, 99% of the radioactive element will decay between 6 and 7 half lives.

Therefore, option A is the correct answer.

Note: Half life of a radioactive element does not give the actual time for its decay to half of initial value, but half life means that the probability of a radioactive element to decay in its half is 50%.