Question

4 × 10²³ tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3 y. Find (a) the activity of the sample, (b) the number of decay in the next 10 hours (c) the number of decays in the next 6.15 y.

Answer 1

Given:
Number of tritium atoms, N₀ = 4 × 10²³
Half-life of tritium nuclei, `T_"1/2"`= 12.3 years

Disintegration constant, `lambda = 0.693/T_"1/2" = 0.693/12.3  "years"^-1`

Activity of the sample (A)is given by 

`A_0 = "dN"/"dt" = lambdaN_0`

⇒ `A_0 = 0.693/t_"1/2"N_0`

= `0.693/12.3 xx 4 xx 10^23` disintegration/year

= `(0.693 xx 4 xx 10^23)/(12.3 xx 3600 xx 24 xx 365)` disintegration/sec

= `7.146 xx 10^14` disintegration/sec

(b) Activity of the sample, A = 7.146 `xx` 10¹⁴ disintegration/sec

Number of decays in the next 10 hours= `7.146 xx 10^14 xx 10 xx 3600`

= `257.256 xx 10^17`

= `2.57 xx 10^19`

(c) Number of atoms left undecayed, N = `N_0e^(-lambdat)`

   Here, N₀ = Initial number of atoms

`therefore N = 4 xx 10^23 xx e ^((-0.693)/12.3 xx 6.15) = 2.83 xx 10^23`

Number of atoms disintegrated = `(N_0 - N) = (4 - 2.83) xx 10^23 = 1.17 xx 10^23`