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

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Correct answer: C. 7.5 × 10 ^ 21

∵ 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

Let N _ β be the number of β particle emitted by 1gram of Na ^ 24...

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