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 = N0 / 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
N0 = 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
⇒ 2n = 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.
\(\lambda = \frac{{2.303}}{t} \times \log \left( {\frac{{{N_0}}}{N}} \right)\)