Answer:
23.5 days
Step-by-step explanation:
The equation for radioactive decay is given by
N = N₀exp(-λt). To find the decay constant, λ, we have
λ = -(lnN/N₀)/t here t = half-life of Neptunium-239 = 2.35 days and N/N₀ = 1/2 where N = Quantity of Neptunium-239 after half-life, N₀ = Initial quantity of Neptunium-239
So, λ = -(ln(1/2))/2.35 = 0.294/day.
Now for Neptunium-239 to decay to 0.100 % of its initial value,
N/N₀ × 100 % = 0.100%
N/N₀ = 0.100/100
N/N₀ = 0.001
From the equation for radioactive decay, we find the time it takes for Neptunium-239 to decay to this value. So, making t subject of the formula,
t = -(lnN/N₀)/λ = -(ln(0.001))/0.294/day = 23.5 days