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The half life period of 84PO210 is 140 days, on disintegration 1.0 g of polonium will remain 0.25 g after.
1. 140 days
2. 280 days
3. 420 days
4. 70 days

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Correct Answer - Option 2 : 280 days

Concept:

Half-life period:

  • It is the time required for the decay of one-half of the number of species.
  • Represented as t½.
  • The expression for the calculation of the amount of radioactive substance left after n half-lives:​
N = N/ 2n

Where, n = no. of half-lives

n  = Total time (t) / Half-life period (t½)

N = Amount of radioactive substance left after n- half-live

N= Initial concentration of the substance            

Calculations:

Given:  t½ = 140 days ; N0 = 1.0 g ; N = 0.25 g

To find: t =?

We know, N = N0 / 2n

 ⇒ 0.25 = 1 / 2n

 ⇒ 2= 4   (·.· 22 = 4)

 ⇒  n = 2 days

Also, n = Total time (t) / Half-life period (t½)

⇒ 2 = t / 140

t = 280 days

Hence, Total time for the disintegration of 1 g Po to 0.25 g is 280 days.

            

  • The half-life period depends only on the decay constant and independent of the amount of radioactive substance.
  • The smaller the half-life of a radionuclide, the greater is its instability.

\({t_½} = \frac{{0.693}}{{\lambda}}\)

Where, λ = decay constant / disintegration constant of the species.

\(\lambda = \frac{{2.303}}{t} \times \log \left( {\frac{{{N_0}}}{N}} \right)\)

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