Question

Calculate the radiation dosage (in grays) for an 75-kg person that is exposed for 5.0 seconds to a 3.0 Ci source of beta radiation. Assume that 100% of the radiation is absorbed and each beta particle has an energy of 2.0× 10–13 J.

Answer is not: 2.15*10^13Gy

Answer is not: 2.15*10^-15 J/kg

Answer is not: 1.1*10^11

Answer 1

1 Ci = 3.7 *10¹⁰ Decay per Second

3.0 Ci = 3 * 3.7 * 10¹⁰ Decay per Second = 1.11 * 10¹¹ Decay per Second.

This radiation is applied for 5.0 second.

So, radiation applied is 5.0 * 1.11 * 10¹¹ Decay = 5.55 * 0¹¹ Decay.

Energy associated with 1 Decay is 2.0 * 10^-13 J / Decay.

Thus energy applied is (5.55 * 0¹¹ Decay) * 2.0 * 10^-13 J / Decay = 0.111 J

Mass is 75 kg

So, energy per unit mass is calculated as

   0.111 J / 75 kg = 0.00148 J/kg = 0.00148 Gray