Question

***After 42 days, 2 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-322

Answer 1

The answer is the half life of phosphorus-32 is of 14 days .

What is Half Life ?

The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay.

The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.

Mass of atoms initially,

N₀ =2.0 g

Mass after 42 days,

N =0.25 g

mass left undecayed we have,

$\rm\dfrac{N}{N_{0}} = \dfrac{1}{2^{n}}$

where  n  is number of half lives occured (the number of times it disintegrated into half of original)

$\rm\dfrac{0.25}{2} = \dfrac{1}{2^{n}}$

$\rm\dfrac{1}{8} = \dfrac{1}{2^{n}}$

$\rm\dfrac{1}{2^{3}} = \dfrac{1}{2^{n}}$

n= 3

number of half lives occured in 42 days is 3

if half life is  $\rm t_{\frac{1}{2} }$

then

3* (  $\rm t_{\frac{1}{2} }$  )  = 42

$\rm t_{\frac{1}{2} }$ = 14 days

Therfore the half life of phosphorus-32 is of 14 days .

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