Question

A $6.95$ gram sample of radioactive ${\text{nobelium}} - 259$ has a half-life of $58$ min. How much is left after $2{\text{ hours and 54 minutes}}$ ?
(A) $10.43$ grams
(B) $0.434$ grams
(C) $3.48$ grams
(D) $1.74$ grams
(E) $0.869$ grams

Answer 1

The act of emitting radiation spontaneously is called radioactivity. This is done by an unstable atomic nucleus that wants to give up some energy to gain a more stable configuration. Radioactive decay happens when an atom has an unstable nucleus like when it has too many neutrons compared to protons or too many protons compared to neutrons. The atom ejects alpha or beta particles, based on the type of radiation and starts losing mass ( in case of alpha particles) to form a stable isotope.

Complete answer:
In radioactivity, half-life is defined as the interval of time required for half of an isotope of a radioactive sample to change into another isotope. It is commonly used to describe how fast an unstable atom undergoes radioactive decay or how long the stable atoms survive.
Given total time= $2{\text{ hours and 54 minutes}}$
Convert this time into minutes.
$1$ hour is $60$ minutes.
$2{\text{ hours and 54 minutes}}$ is $2 \times 60 + 54 = 174$ minutes
The half-life period is $58$ minutes.
The number of half-life periods $= \dfrac{{174}}{{58}} = 3$
After $2{\text{ hours and 54 minutes}}$ , the amount left is $\dfrac{{6.95}}{{{2^3}}} = 0.869{\text{ g}}$
Therefore, option E is the correct answer.

Note:
In a radioactive process, the nuclide which undergoes decay is called parent nuclide and the nuclide produced in this process is called daughter nuclide. In a second-order reaction, the half-life is inversely proportional to the initial concentration of the reactant in the chemical reaction. Half-life is a very useful and interesting aspect of radioactive decay.