Law of Radioactive Decay

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

Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus

The isotope \[\ce{^57Co}\] decays by electron capture to \[\ce{^57Fe}\] with a half-life of 272 d. The \[\ce{^57Fe}\] nucleus is produced in an excited state, and it almost instantaneously emits gamma rays.
(a) Find the mean lifetime and decay constant for ⁵⁷Co.
(b) If the activity of a radiation source ⁵⁷Co is 2.0 µCi now, how many ⁵⁷Co nuclei does the source contain?

c) What will be the activity after one year?

In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following particles is emitted in the decay?

Obtain the relation between the decay constant and half life of a radioactive sample.

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t_1/2. Show that after a time t >> t_1/2 the number of active nuclei will become constant. Find the value of this constant.

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year ______.

Write symbolically the process expressing the β⁺ decay of `""_11^22Na`. Also write the basic nuclear process underlying this decay.