Question

1. The half-life of ²²₁₁Na is 950 days. What is its decay constant? Express your answer in s^?1.

2.The isotope ⁸⁷₃₇Rb decays by beta emission. What nucleus is produced?

Answer 1

(1) Given half life , T1/2 = 950 days

                                      = 950 day x 24 (hr/day) x 60 ( min/hr) x 60 (s/min )

                                      = 82.08x10 ⁶ s

Decay constant , $\lambda =\frac{0.693}{T_{\frac{1}{2}}}=\frac{0.693}{82.08\times 10^{6}}s^{-1}$

                           $\lambda =8.44\times 10^{-9}s^{-1}$

(2) While balancing the nuclear reaction , the sum of the atomic numbers of the reactants is equal to the sum of the atomic numbers of the products.

Similarly the sum of the atomic masses of the reactants is equal to the sum of the atomic masses of the products.

                   $_{37}^{87}\textrm{Rb}\rightarrow _{38}^{87}\textrm{Sr}+_{-1}^{0}\textrm{e}$

                                               beta particle

So the nucleus produced is Stronsium nucleus with atomic number 38 & atomic mass 87.