Final answer:
It will take approximately 5.42 days for 10kg of Np-238 to decay to 4.5kg of Pu-238.
Step-by-step explanation:
To calculate the time it will take for 10kg of Np-238 to decay to 4.5kg of Pu-238, we can use the concept of half-life. The half-life of Np-238 is given as 2.12 days. We can use the formula:
Nt = No * (1/2)^(t/t1/2)
where Nt is the final amount, No is the initial amount, t is the time, and t1/2 is the half-life.
Plugging in the values, we get:
4.5kg = 10kg * (1/2)^(t/2.12)
Solving for t, we find that it will take approximately 5.42 days for 10kg of Np-238 to decay to 4.5kg of Pu-238.