A 100mg sample of Beryillium 11 decays by 4.9% of its previous mass every second. Determine the half-life of Beryillium-11.

Answer 1

To determine the half-life of Beryllium-11, we need to find the time it takes for the sample to decay to 50 mg.

Let the mass of the sample at time t be M(t) mg.
According to the given information, the mass of the sample at time t+1 second is 0.951 M(t) mg since it decays by 4.9% of its previous mass every second.
Therefore, we can write the following equation:

M(t+1) = 0.951 M(t)

Let's calculate the mass of the sample after t seconds using this equation:
M(t+1) = 0.951 M(t)
M(t+2) = 0.951 M(t+1) = (0.951)^2 M(t)
M(t+3) = 0.951 M(t+2) = (0.951)^3 M(t)
...
M(t+n) = (0.951)^n M(t)

Since the mass of the sample at time t+n is M(t+n) = 50 mg when it decays to half its original mass, we can write the equation:

M(t+n) = (0.951)^n M(t) = 50

Substituting M(t) = 100 mg into the equation:
(0.951)^n * 100 = 50

Dividing both sides by 100:
(0.951)^n = 0.5

Taking the logarithm of both sides to solve for n:
n * log(0.951) = log(0.5)

Dividing both sides by log(0.951):
n = log(0.5) / log(0.951)

Using a calculator to find the value of n:
n ≈ 12.96

Therefore, the half-life of Beryllium-11 is approximately 12.96 seconds.