The decay rate of radium at any time t is proportional to its mass at that time. Find the time when the mass will be halved of its initial mass.

The rate of disintegration of a radioactive element at any time t is proportional to its mass at that time. Find the time during which the original mass of 1.5 g m will disintegrate into its mass of 0.5 gm.

In a reaction the rate of reaction is proportional to its active mass, this statement is known as

It is known that the decay rate of radium is directly proportional to its quantity at each given instant.Find the law of variation of a mass of radium as a function of time if at t=0, the mass of the radium was m_(0) and during time t_(0)alpha% of the original mass of radium decay.

The rate of decay of the mass of a radioactive substance at any time is k times its mass at that time. The differential equation satisfied by the mass of the substance is

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

The rate of decay of the mass of a radioactive substance at any time is 10^(-4) times its mass at that instant. After 10000 years, the mass will be

In the previous problem, if time period, T =2(pi) m/(BQ) where Q is the charge of the particle and m is its mass, the ratio of time spent by the particle in field when (theta) is positive to when (theta) is negative is given by

If a point is moving in a line so that its velocity at time t is proportional to the square of the distance covered, then its acceleration at time t varies as

If the escape velocity of a planet is 3 times that of the earth and its radius is 4 times that of the earth, then the mass of the planet is (Mass of the earth = 6 xx 10^24 kg )

A radioactive elements has a half life of 2500 yrs. In how many years will its mass decay by 90% of its initial mass?