Inverse Square
Ruel
1
1
2
2
X (D )
=
X (D )
2
2
1
X = Measured exposure rate
1
D = Distance from source for the measured exposure rate
2
2
X = Exposure rate to be calculated
2
D = New distance from the source
2
Applying the Inverse Square
Rule
to Dose Reduction
Given: A high activity source at an unknown distance.
Find:
Exposure rate from the source at 30 cm without
approaching closer to the source.
2
X is measured exposure rate at distance Y
3
X is measured exposure rate at distance Y + 100 cm
2
3
X (Y)
=
X (Y + 100 cm)
2
2
3
2
Y
=
X (Y + 100 cm) / X
2
2
Set up this equation by entering the exposure rates you
measured at distances Y and Y + 100 cm
Let us assume 100 mr/hr and 50 mr/hr for those two points.
Y =
50 (Y + 100 cm) / 100
=
0.5Y + 100Y + 5,000
2
2
2
simplify this to Y - 200Y - 10,000
=
0
2
This quadratic equation can be factored into two answers.
The positive answer for Y is 241.42 cm.
2
Now we know the distance for exposure rate X and we can
calculate the exposure rate at any distance.
The exposure rate at 30 cm would be 6,476 mR/hr but we
were able to calculate that exposure rate without entering the
High Radiation Area.
A simpler method without having to factor a quadratic equation
is to back AWAY from the source until the exposure rate is 1/4
of the initial rate. The distance you moved away is equal to the
original distance to the source. Now you can use the inverse
square law to calculate the 30 cm exposure rate.
63
Inverse Square
Rule
1
1
2
2
X (D )
=
X (D )
2
2
1
X = Measured exposure rate
1
D = Distance from source for the measured exposure rate
2
2
X = Exposure rate to be calculated
2
D = New distance from the source
2
Applying the Inverse Square
Rule
to Dose Reduction
Given: A high activity source at an unknown distance.
Find:
Exposure rate from the source at 30 cm without
approaching closer to the source.
2
X is measured exposure rate at distance Y
3
X is measured exposure rate at distance Y + 100 cm
2
3
X (Y)
=
X (Y + 100 cm)
2
2
3
2
Y
=
X (Y + 100 cm) / X
2
2
Set up this equation by entering the exposure rates you
measured at distances Y and Y + 100 cm
Let us assume 100 mr/hr and 50 mr/hr for those two points.
Y =
50 (Y + 100 cm) / 100
=
0.5Y + 100Y + 5,000
2
2
2
simplify this to Y - 200Y - 10,000
=
0
2
This quadratic equation can be factored into two answers.
The positive answer for Y is 241.42 cm.
2
Now we know the distance for exposure rate X and we can
calculate the exposure rate at any distance.
The exposure rate at 30 cm would be 6,476 mR/hr but we
were able to calculate that exposure rate without entering the
High Radiation Area.
A simpler method without having to factor a quadratic equation
is to back AWAY from the source until the exposure rate is 1/4
of the initial rate. The distance you moved away is equal to the
original distance to the source. Now you can use the inverse
square law to calculate the 30 cm exposure rate.
63
Inverse Square
Rule
1
1
2
2
X (D )
=
X (D )
2
2
1
X = Measured exposure rate
1
D = Distance from source for the measured exposure rate
2
2
X = Exposure rate to be calculated
2
D = New distance from the source
2
Applying the Inverse Square
Rule
to Dose Reduction
Given: A high activity source at an unknown distance.
Find:
Exposure rate from the source at 30 cm without
approaching closer to the source.
2
X is measured exposure rate at distance Y
3
X is measured exposure rate at distance Y + 100 cm
2
3
X (Y)
=
X (Y + 100 cm)
2
2
3
2
Y
=
X (Y + 100 cm) / X
2
2
Set up this equation by entering the exposure rates you
measured at distances Y and Y + 100 cm
Let us assume 100 mr/hr and 50 mr/hr for those two points.
Y =
50 (Y + 100 cm) / 100
=
0.5Y + 100Y + 5,000
2
2
2
simplify this to Y - 200Y - 10,000
=
0
2
This quadratic equation can be factored into two answers.
The positive answer for Y is 241.42 cm.
2
Now we know the distance for exposure rate X and we can
calculate the exposure rate at any distance.
The exposure rate at 30 cm would be 6,476 mR/hr but we
were able to calculate that exposure rate without entering the
High Radiation Area.
A simpler method without having to factor a quadratic equation
is to back AWAY from the source until the exposure rate is 1/4
of the initial rate. The distance you moved away is equal to the
original distance to the source. Now you can use the inverse
square law to calculate the 30 cm exposure rate.
63
Inverse Square
Rule
1
1
2
2
X (D )
=
X (D )
2
2
1
X = Measured exposure rate
1
D = Distance from source for the measured exposure rate
2
2
X = Exposure rate to be calculated
2
D = New distance from the source
2
Applying the Inverse Square
Rule
to Dose Reduction
Given: A high activity source at an unknown distance.
Find:
Exposure rate from the source at 30 cm without
approaching closer to the source.
2
X is measured exposure rate at distance Y
3
X is measured exposure rate at distance Y + 100 cm
2
3
X (Y)
=
X (Y + 100 cm)
2
2
3
2
Y
=
X (Y + 100 cm) / X
2
2
Set up this equation by entering the exposure rates you
measured at distances Y and Y + 100 cm
Let us assume 100 mr/hr and 50 mr/hr for those two points.
Y =
50 (Y + 100 cm) / 100
=
0.5Y + 100Y + 5,000
2
2
2
simplify this to Y - 200Y - 10,000
=
0
2
This quadratic equation can be factored into two answers.
The positive answer for Y is 241.42 cm.
2
Now we know the distance for exposure rate X and we can
calculate the exposure rate at any distance.
The exposure rate at 30 cm would be 6,476 mR/hr but we
were able to calculate that exposure rate without entering the
High Radiation Area.
A simpler method without having to factor a quadratic equation
is to back AWAY from the source until the exposure rate is 1/4
of the initial rate. The distance you moved away is equal to the
original distance to the source. Now you can use the inverse
square law to calculate the 30 cm exposure rate.
63
