Answer to Question #166257 in General Chemistry for koo

Question

Strontium-90 is a dangerous by-product of atomic testing because it mimics the action of calcium in the body. It decay in two β-emissions to give zirconium-90 (nuclear mass = 89.8824 g).

a) Write a balanced nuclear equation for the overall decay of Sr-90.

b) Calculate ∆m in grams when one mole of Sr-90 decays to Zr-90.

c) How much energy (in KJ) is given off by the decay of 6.50 mg of Sr-90?

Answer 1

a) the balanced nuclear equation for the overall decay of Sr-90.

⁹⁰Sr₃₈ -------> ⁹⁰Zr₄₀ + 2 ⁰β_–1

b) 

m_Sr = 89.8869 amu

m_Zr = 89.8824 amu

m_β = 0.00055 amu

∆m = m_Sr – m_Zr– 2m_β

    = 89.8869 amu – 89.8824 amu – (2×0.00055) amu

    = 0.0034 amu

    

1 amu = 1.661 × 10^–24 grams

∆m = 0.0034 amu × 1.661 × 10^–24 g/amu

    = 5.6474×10^–27 grams

     

c) 

6.50 mg = 0.0065 gram

mass of one Sr-90 

= 89.8869 amu × 1.661 × 10^–24 g/amu 

= 1.493×10^–22 gram

Number of atoms in 6.50 mg of Sr-90, N = 0.0065 / (1.493 ×10^–22)

  = 4.3536×10^19 

∆m = 5.6474×10^–27 grams

    = 5.6474×10^–30 Kg

   

Energy for 1 atom of Sr-90

$E = ∆mC²$

  = 5.6474×10^–30×(3×10^8)² joul

  = 5.0823×10^–13 joul

Total energy

 = E × N

 = 5.0823×10^–13×4.3536×10^19 joul

 = 22126301.28 joul

 ≈ 2.213 × 10⁷ joul

 ≈ 2.213×10⁴ KJ