Law of Radioactive Decay

The decay constant of radioactive substance is 4.33 x 10^-4 per year. Calculate its half life period.

When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom ______.

The variation of decay rate of two radioactive samples A and B with time is shown in figure.

Which of the following statements are true?

1. Decay constant of A is greater than that of B, hence A always decays faster than B.
2. Decay constant of B is greater than that of A but its decay rate is always smaller than that of A.
3. Decay constant of A is greater than that of B but it does not always decay faster than B.
4. Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant.

Disintegration rate of a sample is 10¹⁰ per hour at 20 hours from the start. It reduces to 6.3 x 10⁹ per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.

The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

1. Plot the graph of R versus t and calculate the half-life from the graph.
2. Plot the graph of ln `(R/R_0)` versus t and obtain the value of half-life from the graph.

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of ¹⁴C per gram per minute. A sample from an ancient piece of charcoal shows ¹⁴C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ¹⁴C is 5730 y.

Draw a graph showing the variation of decay rate with number of active nuclei.

The Q value of a nuclear reaction \[\ce{A + b → C + d}\] is defined by

Q = [ m_A+ m_b− m_C− m_d]c² where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]

Atomic masses are given to be

`"m"(""_1^2"H")` = 2.014102 u

`"m"(""_1^3"H")` = 3.016049 u

`"m"(""_6^12"C")` = 12.000000 u

`"m"(""_10^20"Ne")` = 19.992439 u