Can you answer this question with work please?

Question

a substance has a half-life of 50 years if 300 kilograms are present initially how much will remain after 15 years?

Answer 1

Defining whether it is a zeroth, first, second (...etc.) decay is very important to solve the problem.

I am going to assume it is a 1st order decay.

 

Equation for half life for a first order decay is given by:

k*t_1/2 = ln(2)

 

where k is the decay constant

t_1/2 is the half life

 

To find the mass, M, present at time, t, we need to know the initial mass, M₀ and k.

 

k = ln(2)/t_1/2 = ln2/50 ≈ 0.0139

 

ln(M) = ln(M₀) - kt

Now we just substitute our numbers into the equation above:

 

ln(M) = ln(300) - 0.0139*15

ln(M) = 5.496

 

Now recall ln(x) really has a base 'e'. 

ln_e(M) = 5.496

 

take exponent of both sides of the equation:

M = e^5.496 = 243.68 kg ≈244 kg

 

I hope this helps you understand how to approach this kind of problem Azza.