Physics, 28.01.2020 06:31, pikapika24

What is the half-life of a radioisotope

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It is the time after which a given sample of radioactive substance will decay to half of the initial number present in the sample.

Explanation:

As we know that as per law of radioactivity the number of radioactive nuclei present in the sample is proportional to the rate of decay

so it is given by

$\frac{dN}{dt} = -\lambda N$

after solving above relation we will have

$N = N_0e^{-\lambda t}$

now here we know that as the number of nuclei is reduced to half of the initial number then we have

$\frac{N_0}{2} = N_0e^{-\lambda t}$

$t = \frac{ln2}{\lambda}$

so this time is known as half life where the denominator of the equation is known as decay constant.

answered: Guest

Pretty sure the answer is b : )

answered: Guest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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