24.122 CP - Chemistry: Molecular Nature Of Matter And Change

Question

How long can a 54-Ib child be exposed to 1.0 mCi of radiation from ²²²Rn before accumulating 1.0 mrad if the energy of each disintegration is 5.59MeV ?

Step-by-Step Solution

Answer

It will take7.4079 sec too be exposed.

Step 1: Definition of Radiation

The emission and propagation of energy in the form of waves, rays, or particles is known as radiation.

Step 2: Converting MeV into J

The becquerel (Bq) is the SI unit of radioactivity, defined as one disintegration per second $(d/s):1Bq = 1d/s$ . The curie (Ci) is a significantly bigger and more common unit of radioactivity, initially defined as the number of disintegrations per second in 1g of radium-226, but now a fixed quantity:  

$1Ci = 3.7x{10}^{10}\frac{ di\sin t }{\sec }$

The millicurie (mCi) and microcurie (mCi) are regularly encountered since the curie is so enormous. A sample's radioactivity is frequently expressed as a particular activity, or the decay rate per gramme.

Binding energies are often measured in millions of electron volts, or mega-electron volts (MeV):

$1MeV = {10}^{6}eV = 1.602x{10}^{-13}J$

Step 3: Calculating time at which child be exposed

$Time = 7.4079\sec$

$Mass = 54lb\left(\frac{1kg}{2.2lb}\right) = 24.5455kg$

$Energy = 1mCi\left(\frac{{10}^{-3}}{1mCi}\right)\left(\frac{3.70x{10}^{10}\frac{ di\sin t. }{ \sec }}{1Ci}\right)\left(\frac{5.59MeV}{1 di\sin t. }\right)\left(\frac{1.602x{10}^{-13}J}{1MeV}\right)$

$Energy = 3.3134x{10}^{-5}\frac{J}{s}$

$Time = 1mrad\left(\frac{{10}^{-3}}{1mrad}\right)\left(\frac{0.01 \frac{J}{kg}}{1 rad}\right)\left(\frac{24.5455 kg}{3.3134x{10}^{-5}\frac{J}{\sec }}\right)$

$Time = 7.4079\sec$