Question

Calculate the radiation dosage (in grays) for a 63‑kg person who is exposed for 5.0 s to a 3.0 Ci source of beta radiation. Assume that 100% of the radiation is absorbed and that each beta particle has an energy of 1.5×10−13 J.

Answer 1

Answer:

1.32142x10^-3 Gy

Explanation:

Mass m = 63kg

Time t = 5.0s

Beta energy = 1.5x19^-13J

1 Ci = 3.7x10¹⁰

3.0Ci = 3x3.7x10¹⁰

= 11.1x10¹⁰decay/s

We have a total of 11.1x10¹⁰ beta particles produced per second

The question says there is 100% absorption

Et = (11.1x10¹⁰)x5x1.5x10^-13

= 0.08325

The radiation dose = Et/m

= 0.08325/63 kg

= 0.001321428J/kg

= 0.001321428 grays

Or 1.32142x10^-3 Gy

Answer 2

The radiation dose of the person is 1.31 x 10⁻⁴ J/kg.

Radiation dose

The radiation does is the ratio of the total dose to the mass of the person exposed to the radiation.

3 Ci beta radiation = 3 x (3.7x10¹⁰) = 11.1 x 10¹⁰decay/s

Total beta energy absorbed in 5 s

Et = (11.1x10¹⁰) x 5 x 1.5 x 10⁻¹³

Et = 8.25 x 10⁻³ J

Radiation dose of the person is calculated as follows;

Rd = Et/m

Rd = (8.25 x 10⁻³ J) / 63

Rd = 1.31 x 10⁻⁴ J/kg

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