a) The radioactive decay equation for Thorium-232 is:
Th-232 --> He-4 + Ra-228
b) The radioactive decay constant (λ) for Thorium-232 can be calculated using the half-life formula:
t1/2 = (ln 2) / λ
Rearranging the formula, we get:
λ = (ln 2) / t1/2
λ = (ln 2) / 1.4*10^10 years = 4.95*10^-11 per year
The radioactive radiation activity (A) of 10 g of Thorium-232 can be calculated using the following formula:
A = λ * N
Where N is the number of atoms of Thorium-232 in 10 g of Thorium. The number of atoms can be calculated using Avogadro's number (6.02*10^23 atoms per mole) and the molar mass of Thorium-232 (232 g per mole):
N = (10 g / 232 g per mole) * (6.02*10^23 atoms per mole) = 2.60*10^22 atoms
Therefore, the radioactive radiation activity is:
A = 4.95*10^-11 per year * 2.60*10^22 atoms = 1.29*10^12 decays per second
c) After 10 years, the activity of Thorium-232 will decrease due to radioactive decay. The remaining activity can be calculated using the following formula:
A = A0 * e^(-λt)
Where A0 is the initial activity, λ is the decay constant, t is the time elapsed, and e is the base of the natural logarithm (2.718).
The initial activity (A0) is the activity calculated in part b:
A0 = 1.29*10^12 decays per second
The time elapsed (t) is 10 years.
Therefore, the remaining activity is:
A = A0 * e^(-λt) = 1.29*10^12 decays per second * e^(-4.95*10^-11 per year * 10 years) = 1.09*10^12 decays per second
Therefore, the activity after 10 years is 1.09*10^12 decays per second.