A laboratory rat weighs 265 g and absorbs 1.57 × 10¹⁰ β⁻ particles, each with an energy of 2.20 × 10⁻¹³ J.

 

(a) How many rads does the animal receive?

 

(b) What is the dose in Gy?

 

(c) If the RBE is 0.75, what is the equivalent dose in Sv?

(a) How many rads does the animal receive?

rads = 1.30 rads

(b) What is the dose in Gy?

Dose in Gy = 0.013 Gy

(c) If the RBE is 0.75, what is the equivalent dose in Sv?

Sv = Gy × RBE = 0.013 Gy x 0.75 = 9.75x10^-3 rem

A laboratory rat weighs 265 g and absorbs 1.57 × 1010 β− particles, each with an energy of 2.20 × 10−13 J.

(a) How many rads does the animal receive?

1 rad is equivalent to 0.01 J/kg

First convert the given mass into kg

mass in kg = 265 g x (1 kg / 1000 g) = 0.265 kg

Calculate the energy of 1.57x10¹⁰ B- particles in Joule

Energy in Joule = 1.57x10¹⁰ β^- particles x (2.20 × 10^-13 J / 1 β^- particle) = 3.45x10^-3 J

Now, calculate the number of rads

rads = ( 3.45x10^-3 J /0.265 kg) x (1 rad / 0.01 J/kg) = 0.0130 J/kg x (1 rad kg/ 0.01 J) = 1.30 rads

(b) What is the dose in Gy?

1 rad is equivalent to 0.01 Gy

Dose in Gy = 1.30 rads x (0.01 Gy/ 1 rad) = 0.013 Gy

(c) If the RBE is 0.75, what is the equivalent dose in Sv?

The sievert (Sv) is defined to be Sv = Gy × RBE

where,

Gy = gray = 0.013 Gy

RBE = relative biological effectiveness = 0.75

Therefore, Sv = 0.013 Gy x 0.75 = 9.75x10^-3 rem

rem = roentgen equivalent man