Alpha particles with RBE, energy question

[FlipStyle1308]

Homework Statement

Alpha particles with an RBE of 13 deliver a 53 mrad whole-body radiation dose to a 65 kg patient.
(a) What dosage, in rem, does the patient receive?
(b) How much energy is absorbed by the patient (in mJ)?

Homework Equations

dose in rem = dose in rad x RBE

The Attempt at a Solution

I correctly answered part (a), getting 0.689J/kg as my answer. For part (b), I then multipled the answer from (a) by 65kg, which equals 44.785 J, or 44,785 mJ. However, my answer is incorrect. Is there something I am missing? Thanks.

 

[OlderDan]

Homework Statement

Alpha particles with an RBE of 13 deliver a 53 mrad whole-body radiation dose to a 65 kg patient.
(a) What dosage, in rem, does the patient receive?
(b) How much energy is absorbed by the patient (in mJ)?

Homework Equations

dose in rem = dose in rad x RBE

The Attempt at a Solution

I correctly answered part (a), getting 0.689J/kg as my answer. For part (b), I then multipled the answer from (a) by 65kg, which equals 44.785 J, or 44,785 mJ. However, my answer is incorrect. Is there something I am missing? Thanks.

My guess is you should be using rads for part b, since that is the measure of the actual energy, while rem is some attempt to quantify the damage caused by a certain amount of energy absorption.

 

[daveb]

Part a) should still be in units of rem so that it is apparent that this is absorbed dose in a human. For part b), the actual energy that is absorbed has nothing to do with the RBE. RBE is only a measure of a tissue's sensitivity to a type of radiation, not an energy (well, except for neutrons which have varying RBEs depending on neutron energy).

 

[FlipStyle1308]

Part a) should still be in units of rem so that it is apparent that this is absorbed dose in a human. For part b), the actual energy that is absorbed has nothing to do with the RBE. RBE is only a measure of a tissue's sensitivity to a type of radiation, not an energy (well, except for neutrons which have varying RBEs depending on neutron energy).

So what equation should I be using? My book only gives me:
RBE = (dose of 200-kV X-rays necessary to produce a given biological effect)/(dose of a particular type of radiation necessary to produce the same biological effect)
and dose in rem = dose in rad X RBE

 

[OlderDan]

So what equation should I be using? My book only gives me:
RBE = (dose of 200-kV X-rays necessary to produce a given biological effect)/(dose of a particular type of radiation necessary to produce the same biological effect)
and dose in rem = dose in rad X RBE

It should also give you the definition of a rad as 0.01 Joules per kilogram of mass.

http://www.unc.edu/~rowlett/units/dictR.html

 

[FlipStyle1308]

It should also give you the definition of a rad as 0.01 Joules per kilogram of mass.

http://www.unc.edu/~rowlett/units/dictR.html

Hmm, thanks. So (68.9 rad)(13) = 895.7 J/kg
895.7 J/kg x 65 kg = 58220.5 J = 58220500 mJ?

 

[OlderDan]

Hmm, thanks. So (68.9 rad)(13) = 895.7 J/kg
895.7 J/kg x 65 kg = 58220.5 J = 58220500 mJ?

There is no 13. 53mrad = 53*.01 mJ/kg (the m in mJ comes from the m in mrad). Multiply that by the body mass and you get mJoules of energy. The RBE of 13 means that this much energy from alpha particles is more damaging than the reference radiation that corresponds to RBE = 1, but it does not change the actual energy absorption.

 

[FlipStyle1308]

There is no 13. 53mrad = 53*.01 mJ/kg (the m in mJ comes from the m in mrad). Multiply that by the body mass and you get mJoules of energy. The RBE of 13 means that this much energy from alpha particles is more damaging than the reference radiation that corresponds to RBE = 1, but it does not change the actual energy absorption.

So my answer should be 3445 mJ? It's still incorrect.

 

[OlderDan]

So my answer should be 3445 mJ? It's still incorrect.

That is not correct. You left out the factor of 0.01

It is 53 mrad * .01 J/kg/rad * 65 kg

 

[FlipStyle1308]

Oh, so 34.45 mJ?

 

[FlipStyle1308]

Bump, can someone please check my answer?

 

[OlderDan]

Bump, can someone please check my answer?

Do you really need someone to confirm that you multiplied correctly?

That is not correct. You left out the factor of 0.01

It is 53 mrad * .01 J/kg/rad * 65 kg

 

[FlipStyle1308]

Do you really need someone to confirm that you multiplied correctly?

Sorry, I was running out of attempts on WebAssign, and didn't want to risk it by misinterpreting your advice. Thank you!