A Li 7 target is bombarded with a proton beam current of magnitude 10 - 4 A for an hour to produce Be 7 of activity 1 . 8 × 10 8 disintegrations per second. If we assume that one radioactive nucleus of beryllium is produced by bombarding 1000 protons, then its half-life is close to

Step-by-step solution

At time t , let say there are N atoms of Be 7 (radioactive). Then the net rate of formation of Be 7 nuclei at this instant is, d ⁡ N ⁡ d ⁡ t = 1 0 - 4 1 . 6 × 1 0 - 1 9 × 1 0 0 0 - λ N ⁡ or d ⁡ N ⁡ d ⁡ t = 6 . 2 5 × 1 0 1 1 - λ N ⁡ or ∫ o ⁡ N ⁡ 0 d ⁡ N ⁡ 6 . 2 5 × 1 0 1 1 - λ N ⁡ = ∫ 0 3 6 0 0 d ⁡ t where N 0 are the number of nuclei at   t   =   1   hour or 3600 &#1