Let N β be the number of β particle emitted by 1 gram of Na 24 radioactive nuclei having a half life of 15 h . In 7 . 5 h , the number N β is close to N A = 6 .023 × 10 23 mole - 1

Step-by-step solution

∵ N N 0 = 1 2 n N = no. of un-decayed nuclei N 0 = initial no. of nuclei Also t = n × T 1 2 ⇒ N N 0 = 1 2 t T 1 2 ⇒ N = N 0 1 2 7.5 15 ⇒ N = N 0 1 2 1 2 ⇒ N = N 0 2   ∴ Number of nuclei decayed = N 0 - N 0 2 = N 0 2 - 1 2 = 0.414 1.414 N 0 = 0.29 N 0 ∵ N 0 = 1 24 × 6.023 × 10 23 ⇒ No. of nuclei decayed = 0.29 × 1 24 × 6.023 × 10 23 = 0.0727 × 10 23 = 7.5 × 10 21