Question

How long can a 44 lb child be exposed to 1.0 mCi of radiation from ²²²Rn before accumulating 1.0 mrad if the energy of each disintegration is 5.59 MeV?

Give answer in seconds.

Answer 1

Following is the - complete Answer -&- Explanation: for the given : Question: - in....Typed Format...

Answer:

Time for which the 44 lb , Child - can be allowed to be exposed to 1.0 mCi , of Radiation: T_allow. = 6.0  seconds

Explanation:

Following is the complete : Explanation, for the above Answer: in.....Typed Format....

• Given:

1. Mass of the child: m_c = 44.0 lb  ( i.e. pounds )
2. Intensity of the Radiation: =  1.0 mCi ( i.e. millicurie ) = 3.70 x 10⁷ disintegrations/ second
3. Energy emitted by each disintegration: E_d = 5.59 MeV ( i.e. milli - electron volts )
4. Rate at which the energy is accumulated from radiation: = 1.0 mrad ( i.e. Millirad )

• ​​​​​​​Step -1:

​​​​​​​First of all let's convert, the given accumulation rate of radiation ( i.e. mrad ) to the J/lb ( i.e. Joule per pound ):

We know: 1.0 mrad = 4.536 x 10^-6 J / lb

Therefore, at 1.0 mrad, the 44.0 lb child , will accumulate :  the following amount of Energy....in Joule ...

  Threshold of Energy accumulation = ( mass of child ) x ( energy absorbed by the child )

= ( 44.0 lb ) x ( 4.536 x 10^-6 J / lb )

= 1.99 x 10^-4 Joule

  Threshold of Energy accumulation =  1.99 x 10^-4 Joule

• Step - 2:

​​​​​​​Now, we will try to determine, energy generated by radioactive emission, per second: ( i.e. using the given information)

We know the following:

1. Energy emitted each disintegration = E_d = 5.59 MeV ( i.e. milli - electron volts )
2. We know:   1.0 MeV = 1.602 x 10^-13 J   ( Joule )
3. We know: since the intensity of radiation: = 1.0 mCi = 3.70 x 10⁷ disintegrations/ second

​​​​​​​ Therefore:  Energy emitted by each disintegration, per second:

= ( 5.59 MeV x 1.602 x 10^-13 J / MeV ) J / disintegration x ( 3.70 x 10⁷ disintegrations / second )

=  3.313 x 10^-5 J / second

• Step - 3:

​​​​​​​Therefore, the time required to reach the threshold of energy accumulation, will be :

T_req. = ( 1.99 x 10^-4 Joule ) / ( 3.313 x 10^-5 J / second ) = 6.0066 seconds 6.0 seconds

• Answer:

​​​​​​​Time for which the child can be exposed: T_req. = 6.0 seconds ( Answer )