One of the nuclides in spent nuclear fuel is u-235 , an alpha emitter with a half-life of 703 million years. how long will take for the amount of u-235 to reach 49.0% of its initial amount?

683 million years

Explanation:

For radioactive nuclides, the time to decay is given by the expression:

t = -2.303 /k log (A/A₀)

where k is the decay constant and is calculated from the equation:

k = 0.693/ t₁/₂  where ₁/₂ is the half-life.

k = 0693/ 703 x 10⁶ yrs = 9.85 x 10⁻¹⁰ /yr

A = amount after time t

A₀ = amount originally present

Then

t = -2.303 / 9.85 x 10⁻¹⁰ /yr x log (0.51) = 683 x 10⁶ yr