To find the new intensity of radiation when changing the distance from the radiographic tube, we utilize the inverse square law of radiation. This law states that the intensity of radiation is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:
[tex]\[ I_1 / I_2 = (D_2 / D_1)^2 \][/tex]
where:
- [tex]\( I_1 \)[/tex] is the initial intensity,
- [tex]\( I_2 \)[/tex] is the new intensity,
- [tex]\( D_1 \)[/tex] is the initial distance, and
- [tex]\( D_2 \)[/tex] is the new distance.
Given:
- [tex]\( I_1 = 95 \)[/tex] C/kg (initial intensity),
- [tex]\( D_1 = 36 \)[/tex] inches (initial distance),
- [tex]\( D_2 = 72 \)[/tex] inches (new distance).
First, we plug the values into the inverse square law formula to find the new intensity [tex]\( I_2 \)[/tex]:
[tex]\[ I_1 / I_2 = (D_2 / D_1)^2 \][/tex]
[tex]\[ 95 / I_2 = (72 / 36)^2 \][/tex]
Next, we compute the ratio of the distances squared:
[tex]\[ (72 / 36)^2 = (2)^2 = 4 \][/tex]
Now, we substitute this back into our formula:
[tex]\[ 95 / I_2 = 4 \][/tex]
We solve for [tex]\( I_2 \)[/tex]:
[tex]\[ I_2 = 95 / 4 \][/tex]
Finally, the new intensity [tex]\( I_2 \)[/tex] is:
[tex]\[ I_2 = 23.75 \][/tex]
Thus, the intensity of radiation at a distance of 72 inches from the radiographic tube will be 23.75 C/kg.
