The activity of a sample of 31Si (T1/2 = 9.43×103 s) is 7.88×105 decays per second. What is the mass of sample present?

To determine the mass of the sample, we need to use the formula for radioactive decay:

Activity = λ * N

Where:
- Activity is the number of decays per second (given as 7.88×105 decays/s)
- λ (lambda) is the decay constant
- N is the number of radioactive particles (unknown)

First, we need to find the decay constant (λ), which can be determined using the half-life (T1/2):

λ = ln(2) / T1/2

Plugging in the given half-life of 31Si (T1/2 = 9.43×103 s):

λ = ln(2) / (9.43×103 s)

Now, we have λ value, and we can solve for N (number of radioactive particles):

Activity = λ * N
7.88×105 decays/s = (ln(2) / (9.43×103 s)) * N

Solving for N:

N = (7.88×105 decays/s) / (ln(2) / (9.43×103 s))

Now that we have the value for N, we can calculate the mass of the sample using the Avogadro's number (6.022 × 10^23 atoms/mol) and the molar mass of 31Si:

Mass = N * (molar mass of 31Si) / Avogadro's number

The molar mass of 31Si is 30.973761998 g/mol.

Now, plug in the values to calculate the mass:

Mass = N * (30.973761998 g/mol) / (6.022 × 10^23 atoms/mol)