Question

How many ${}^{137}\text{Cs}$ need to be present in each $kg$ of body tissue if an equivalent does for one week is $3.55$ $Sv$?

• A. $1.25\times {10}^{-9}$
• B. $1.25\times {10}^{11}$
• C. $1.25\times {10}^{13}$
• D. none

Answer 1

Answer: (C)

$1.25\times {10}^{13}$

$3.5$ $Sv$ = $RBE\times absorbeddose$ $\left(Gy\right)$
Absorbed dose $=\frac{3.5}{1.5}$ $gy$ $=2.33$ $J/kg$

Number of ${}^{137}\text{Cs}$ atoms present
$N_0$ $=\frac{N}{e^{-\lambda t}}$
$N$ $=N_0{e}^{-\lambda t}$
$N$ $=\frac{2.33}{1.17\times 1.6\times {10}^{-13}}$
$=\frac{2.33\times {10}^{13}}{1.17\times 1.6}$ = $1.25\times {10}^{13}$