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.

Number of atoms remaining after 2 half lives are 100 atomsNumber of atoms remaining after 3 half lives are 50 atomsNumber of atoms remaining after 4 half lives are 25 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

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The earths atmosphere is made up of nitrogen and oxygensolids turning into gases is called sublimation.

Initial velocity,  u = 4.9 m/sfinal velocity = v m/sinitial height,  h₁ =  245 m    final height, h₂ = 0a = -9.8  m/s²time taken = t secondss = ut + 0.5at²⇒  (h₂-h₁) = ut + 0.5at²⇒  0-245 = 4.9t + 0.5×(-9.8)×t²⇒ -245 = 4.9t - 4.9t²⇒ 4.9t² -4.9t -245 =0solving it, we get   t = 7.59sv  = u +  at = 4.9 -9.8×7.59 = 4.9 - 74.38 = -69.48 m/svelocity is  69.48 m/s downward