Calculate number of photons absorbed

[kuruman]

I see! Since the energy absorbed per kg is 40x1^-4 J, the total absorbed energy is 4x10^-4x1,2 = 4,8x10^-4 Gy = 0,48 mGy?
Would then the number of photons be 4,8x10^-4 [J/kg]/8*10^-15 = 6x10¹⁰ photons?

Yes.

 

[kuruman]

This is a new question. Please post on separate thread with separate title.

 

[jbriggs444]

I see! Since the energy absorbed per kg is 40x1^-4 J, the total absorbed energy is 4x10^-4x1,2 = 4,8x10^-4 Gy = 0,48 mGy?

Ummm. You need to track your units more carefully.

If the energy absorbed per kg is $4 \times 10^{-4}$ J then we multiply by the number of kilograms to get the total energy absorbed, yes. Don't just multiply the numbers. Multiply the units as well.

The unit for total energy absorbed is the Joule, not a Joule per kilogram. If you find yourself expressing energy in milliGrays then you know that you have bungled something.

 

[Steve4Physics]

I see! Since the energy absorbed per kg is 40x1^-4 J, the total absorbed energy is 4x10^-4x1,2 = 4,8x10^-4 Gy = 0,48 mGy?
Would then the number of photons be 4,8x10^-4 [J/kg]/8*10^-15 = 6x10¹⁰ photons?

One mistake (but a very serious one). Others have pointed it out, but I will point it out again!

You cannot say total absorbed energy is [some number] of Gy. It is [some number] of J.

For example if the object's mass is 2kg and the aborbed dose is 3Gy, then the total energy absorbed by the object is 2*3 = 6J. It is not 6Gy.

 

[kuruman]

When I posted #51, I thought, without really thinking, that one cannot get the correct number of photons from the wrong premises. I suspect OP has the same conceptual difficulty as people who, when told that a power plant generates 200 MW, ask "200 MW per what?"
To @Luxdot: Until you get used to the idea of Grays as a unit, should carry the units when multiplying numbers and not put them in only some times. Here is what I mean using the soda can question as an example.

Hourly wage = $W = 15.00~\frac{\text{dollars}}{\text{hour}}$
Hours worked = $T=4~\text{hour}$
Can price = $P=1.20~\frac{\text{dollars}}{\text{can}}$
Formula for solution
$$\text{Number of cans}=\frac{\text{Hours worked}\times \text{Hourly wage}}{\text{Can price}}=\frac{T\times W}{P}.$$ Now $$T\times W \times \frac{1}{P}=4~\cancel{\text{hour}}\times 15.00~\frac{\cancel{\text{dollars}}}{\cancel{\text{hour}}}\times \frac{1}{1.20}~\frac{\text{can}}{\cancel {\text{dollars}}}=50~\text{can(s)}.$$
Let's see you do this using your numerical variables.

 

[Luxdot]

One mistake (but a very serious one). Others have pointed it out, but I will point it out again!

You cannot say total absorbed energy is [some number] of Gy. It is [some number] of J.

For example if the object's mass is 2kg and the aborbed dose is 3Gy, then the total energy absorbed by the object is 2*3 = 6J. It is not 6Gy.

So, since the equivalent dose is 0,40 mSv = 0,0004 Sv and the mass 1,2 kg, the absorbed dose is 0,00048 Gy (or J/kg). To get the total absorbed energy, wouldn't I have to divide the absorbed dose with the mass again to get rid of the kg? I.e. 0,00048 [J/kg] / 1,2 [kg] = 0,00040 [J]? This would mean that the number of photons are 0,00040[J]/8*10^-15[J] = 5*10¹⁰ photons. Given that the energy of one photon is 50 keV or 8*10^-15 J.

 

[Steve4Physics]

So, since the equivalent dose is 0,40 mSv = 0,0004 Sv and the mass 1,2 kg, the absorbed dose is 0,00048 Gy (or J/kg). To get the total absorbed energy, wouldn't I have to divide the absorbed dose with the mass again to get rid of the kg? I.e. 0,00048 [J/kg] / 1,2 [kg] = 0,00040 [J]? This would mean that the number of photons are 0,00040[J]/8*10^-15[J] = 5*10¹⁰ photons. Given that the energy of one photon is 50 keV or 8*10^-15 J.

No. Go through each of the following steps very carefully.

1. The equivalent dose is 0.40mSv = 4x10⁻⁴ Sv.

2. Because we are dealing with X-rays, the 'Q-factor' =1, so

$absorbed \space dose = \frac {equivalent \space dose}{Q-factor} = \frac {4 \times10⁻⁴}{1} = 4\times10⁻⁴ Gy$

Converting from Sv to Gy has nothing to do with the mass.

Note that 4x10⁻⁴ Gy means the same as 4x10⁻⁴ J/kg

3. Then, to get the total energy in joules, you multiply absorbed dose by mass:

E = (4x10⁻⁴ J/kg) x (1.2kg) = 4.8x10⁻⁴J (the ‘kg’ unit cancels giving the answer in joules)

4. Finally, to get the number of photons, you divide E (from step 3) by the energy (in J) of one photon.

(Note. If we were told that we had alpha-radiation rather than X-rays, then the Q-factor would be 20 and the absorbed dose would be 0.40mSv/20 = 0.020mGy. If you then wanted the total energy absorbed (in joules) you would multiply 0.020 by the mass.)

[Edit - typo' corrected.]