Some amount of a radioactive substance (half-life = 10 days ) is spread inside a room and consequently, the level of radiation becomes 50 times the permissible level for normal occupancy of the room. After how many days will the room be safe for occupation?

Step-by-step solution

since, the initial activity is 50 times the activity for safe occupancy, therefore R 0 = 50 R , where R = λ N . since, R ∝ N R R 0 = N N 0 = 1 2 n = 1 2 t / T Or 1 2 t / 10 = 1 50 2 t / 10 - 50 ⇒ t 10 log 10 2 = log 10 50 ⇒    t = 10 log 10 50 log 10 2 = 10 × 1 . 699 0 . 301 = 56 . 4 days