g Consider (12.5 A) micro-grams of a radioactive isotope with a mass number of (78 B) and a half-life of (32.6 C) million years. If energy released in each decay is 32.6 keV, determine the total energy released in joules (J) in 1 (one) year. Give your answer with three significant figures.

Energy released =  18.985 J

Explanation:

The  exponential decay of radioactive substance is given by -

N(t) = N₀

where

N₀ = initial quantity

k = decay constant

Half life,

⇒

Given,

N₀ = 12.5 + 3 = 15.5 × 10⁻⁶ gm

= 32.6 + 18 = 50.6 × 10⁶ years

So,

= 1.361 × 10⁻⁸ year⁻¹

Now,

N(1) = 15.5 × 10⁻⁶  

      = 15.49999978904

Now,

Substance decayed = N₀ - N(t)

                                 = 15.5 × 10⁻⁶ - 15.49999978904 × 10⁻⁶

                                 = 21.095 × 10⁻¹⁷ kg

⇒Δm = 21.095 × 10⁻¹⁷ kg

So,

Energy released = Δmc²

                           = 21.095 × 10⁻¹⁷ × 3 ×10⁸ × 3 × 10⁸

                          = 189.855 ×10⁻¹

                          = 18.985 J

⇒Energy released =  18.985 J

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