A 100mg sample of beryllium 11 decays by 4.9% of its previous mass every second.Determine the half life of beryllium-11(hint:the equation A=A0(1-r)^t may be useful as a starting point
To determine the half-life of beryllium-11, we need to use the equation A = A₀(1 - r)^t, where:
- A is the remaining mass at time t (in this case, A is the mass of the sample after the decay).
- A₀ is the initial mass (100mg in this case).
- r is the decay rate (4.9% or 0.049).
- t is the time elapsed.
Since the half-life is the time it takes for the mass to decrease by half, we can set up the equation as follows:
50 = 100(1 - 0.049)^t
Dividing both sides by 100, we get:
0.5 = (1 - 0.049)^t
Taking the logarithm with base (1 - 0.049) on both sides to solve for t, we have:
log(0.5) = log((1 - 0.049)^t)
Using the logarithmic property, we can bring the exponent down:
log(0.5) = t * log(1 - 0.049)
Solving for t, we divide both sides by log(1 - 0.049):
t = log(0.5) / log(1 - 0.049)
Calculating this using a calculator, we find:
t ≈ 14.5 seconds
Therefore, the half-life of beryllium-11 is approximately 14.5 seconds.