The half-life for the α decay of uranium is 4.47 × 109 yr. determine the age (in years) of a rock specimen that contains 55.5% of its original number of atoms.

Explanation:

Half-life of uranium = years

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = age of sample  = ?

a = let initial amount of the reactant  = 100

a - x = amount left after decay process  =

Now put all the given values in above equation, we get

Thus the age of a rock specimen that contains 55.5% of its original number of atoms is

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards