If we start with 400 atoms of a radioactive substance, how many would remain after one half-life? After 2 half-lives? After 3 half-lives? After 4 half-lives?

The half-life is the time it takes the number of atoms to remain half of the

initial number of atoms.

Reasons:

The initial number of radioactive atoms, N₀ = 400

Required:

The number of atoms that will remain after 2 half lives?

Solution:

Half life is given by the formula;

After 2 half lives, we have;

t = 2 ×

Which gives;

The number of atoms remaining after 2 half lives = 100

After 3 half-lives, we have;

The number of atoms remaining after 3 half lives = 50

After 4 half-lives, we have:

The number of atoms remaining after 4 half lives = 25

Learn more here:

link

link

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west