Question

Assuming that each atom that decays emits one alpha particle, how many alpha particles are emitted per minute by a 0.00562-g sample of ²³¹Pa that is free from its decay products? The half-life of ²³¹Pa is 3.25×10⁴ y and the mass of a ²³¹Pa atom is 231.036 u.

--------------------- alpha particles min^-1

Answer 1

Given

Mass of Pa = 0.00562 g

Half life = 3.25 * 10⁴ yr = 3.25 *  10⁴ * 365.25 * 24 * 60 min = 17.094 * 10⁹ min

In half life mass of Pa will reduce half of the intial mass

Mass after 17.094 * 10⁹ min = 0.00562 /2 = 0.00281 g

Mass of Pa reacted in 1 min = (0.00562 - 0.00281) g / 17.094 * 10⁹ min = 1.644 * 10^-13 g/min

Given molar mass of Pa = 231.036 g/mol

No. of moles of Pa decayed per min = 1.644 * 10^-13 g/min / 231.036 g/mol = 7.115 * 10^-16 mol/min

No of atoms = No. of moles * avogadro number ( 6.023 * 10²³ )

No. of atoms of Pa that decays per min = 7.115 * 10^-16 mol/min * 6.023 * 10²³ = 4.285 * 10⁸ atoms/min

Given each atom Pa emits one alpha particles

so No. of alpha particles emitted per min = 4.285 * 10⁸