Physics – 5.2.1 Detection of radioactivity | e-Consult

1. Calculate the decay constant (λ):

λ = 0.693 / 5.73 years = 0.1216 years^-1

Convert years to seconds: 0.1216 years^-1 * 365.25 days/year * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 1.82 x 10^-7 s^-1

2. Calculate the number of atoms remaining after time t (N(t)):

N(t) = N₀ * e^-λt

Where N₀ is the initial number of atoms (1.6 x 10¹⁰) and t is the time in seconds.

Immediately after collection, t = 0 seconds. Therefore, N(0) = 1.6 x 10¹⁰ atoms.

3. Calculate the decay rate (dN/dt):

dN/dt = -λN(t)

At t = 0, dN/dt = -0.1216 * 1.6 x 10¹⁰ = -1.9456 x 10⁹ atoms/s

4. Calculate the count rate:

Count rate = |dN/dt| * e^-λt

Count rate = 1.9456 x 10⁹ atoms/s * e⁰ = 1.9456 x 10⁹ counts/s

Convert to counts/minute: 1.9456 x 10⁹ counts/s * 60 s/min = 1.167 x 10¹¹ counts/minute

Therefore, the count rate is approximately 1.167 x 10¹¹ counts/minute.