The bacterial growth follows the rate law, `(dN)/(dt) = KN` where 'K' is a constant and 'N' is the number of bacteria cell at any time. If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the initial one.

In a certain culture the rate of increment of bacterial at any instant is proportional to the cube root of the number of bacteria present at that instant. IF the number of bacteria becomes 8 times in 3 hours, in how much time that number becomes 64 times?

In a certain culture, the number of bacteria at any instant increases at a rate proportional to the square root of the number present at that instant. If the number becomes 16 times in 5 hours, when the number will be 49 times?

The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq = 1 decay. s^(-1) . The half-life of Iodine-131 is 8 d. Its mean life (in SI) is - (A) 4.79xx10^5 s. (B) 6.912xx10^5 s. (C) 9.974 xx 10^5 s. (D) 22.96xx10^5 s.

The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq = 1 decay. s^(-1) , The half-life of Iodine-131 is 8d. Its decay constant (in SI) is - (A) 10^(-6) (B) 1.45xx10^(-6) (C) 2xx10^(-6) (D) 2.9xx10^(-6)

The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq = 1 decay. s^(-1) . The half-life of Iodine-131 is 8 d. What is the activity (in Bq) of 1 g of Iodine? (A) 2.3xx10^15 (B) 4.6xx10^15 (C) 6.9xx10^15 (D) 9.2xx10^15

The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq = 1 decay. s^(-1) , and Avogadro's number, N=6.023xx10^23 What is the ratio of activity of same amount of sodium-24 to that of iodine-131? [half life of sodium-24 is 15h.] (A) 1/70 (B) 1/7 (C) 7 (D) 70

The initial number of radioactive atoms in a radioactive sample is N_0 . If after time t the number of becomes N, then N=N_0e^(-lambdat) , where lambda is known as the decay constant of the element. The time in which the number of radioactive atoms becomes half of its initial number is called the half-life (T) of the element. The time in which the number of atoms falls to 1/e times of its initial number is the mean life (tau) of the element. The product lambdaN is the activity (A) of the radioactive sample when the number of atoms is N. The SI unit of activity is bequerel (Bq)' where 1 Bq= 1 decay. s^(-1) . After how many days the activity of Iodine-131 will be 1/16 th of its initial value. [The half-life of Iodine-131 is 8 d.] (A) 24 d (B) 32 d (C) 40 d (D) 48 d

A radioactive substance is subject to the law of natural decay (dv)/(dt)=-kv where v is the valume of the substance at time t and k is a positive constant. If 40% of the substance disappear in 25 years, find the time it takes to disappear 60% of the substance.

In a culture of E.coli the cell population increased from 1.5 xx 10^(6) cells/ml to 12 xx 10^(6) cells/ml in 36 minutes. The generation time is

Water is drained from a vertical cylindrical tank by opening a value at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth y, where the constant of proprortionality kgt0 depends on the acceliration due to gravity and the geomety of the hole. If is measured in minutes and k=(1)/(15) then the time of drain the tank, If the water is 4 m deep to start with is