Question

How much time is required for a 6.25 mg sample of 51 cr to decay to 0.85 mg if it has a half life Of 27.8 days

Answer 1

For a first order decay reaction;

ln(A/A°) = - kt

where, A = concentration remained at any time (t) = 0.85mg given.

A° = initial concentration of sample = 6.25mg given .

k = decay constant = 0.693/half life (for Ist order )

t = time = to be determined .

Finding (k) , k = 0.693/27.8days = 0.025 /day

Using all values in equation first ;

ln(0.85mg/6.25mg) = - 0.025/day × t

ln(0.136) = - 0.025/day × t

-2.0 = -0.025/day × t

t = 2 ÷ (0.025/day) = 80 days

Hence it will take 80days for this decay.