inverse square law applied to radiation intensity from a point source Given intensity at distance 1 (I_1) = 329.0 mR/hr; distance 1 (d_1) = 3.1000 m; distance 2 (d_2) = 11.6000 m, determine the intensity at distance 2 (I_2) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_2 is given, so isolate I_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_2:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 329.0 mR/hr, distance 1 (d_1) = 3.1000 m, distance 2 (d_2) = 11.6000 m.

4. Step 4 — Substitute the given values:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{2} = 23.4965\ \text{mR/hr}$$

6. Step 6 — Check: returning I_2 = 23.4965 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 46.9930 — kept a factor of two that cancels in the correct rearrangement.
• 11.7483 — dropped that same factor in the other direction.
• 25.8462 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

inverse square law used to set a safe worker distance from a radioactive source Given distance 1 (d_1) = 2.7000 m; distance 2 (d_2) = 17.0000 m; intensity at distance 2 (I_2) = 324.6 mR/hr, determine the intensity at distance 1 (I_1) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_1 is given, so isolate I_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_1:

   $$I_{1} = I_2\left(\dfrac{d_2}{d_1}\right)^2$$

3. Step 3 — List the givens: distance 1 (d_1) = 2.7000 m, distance 2 (d_2) = 17.0000 m, intensity at distance 2 (I_2) = 324.6 mR/hr.

4. Step 4 — Substitute the given values:

   $$I_{1} = I_2\left(\dfrac{d_2}{d_1}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{1} = 12868\ \text{mR/hr}$$

6. Step 6 — Check: returning I_1 = 12,868 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 25,735 — kept a factor of two that cancels in the correct rearrangement.
• 6,434 — dropped that same factor in the other direction.
• 14,154 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

radiation shielding distance calculated with the inverse square law Given intensity at distance 1 (I_1) = 764.0 mR/hr; distance 1 (d_1) = 1.0000 m; intensity at distance 2 (I_2) = 333.9 mR/hr, determine the distance 2 (d_2) in m.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except d_2 is given, so isolate d_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for d_2:

   $$d_{2} = d_1\sqrt{\dfrac{I_1}{I_2}}$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 764.0 mR/hr, distance 1 (d_1) = 1.0000 m, intensity at distance 2 (I_2) = 333.9 mR/hr.

4. Step 4 — Substitute the given values:

   $$d_{2} = d_1\sqrt{\dfrac{I_1}{I_2}}$$

5. Step 5 — Evaluate:

   $$d_{2} = 1.5126\ \text{m}$$

6. Step 6 — Check: returning d_2 = 1.5126 m to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 3.0253 — kept a factor of two that cancels in the correct rearrangement.
• 0.7563 — dropped that same factor in the other direction.
• 1.6639 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

inverse square law applied to radiation intensity from a point source Given intensity at distance 1 (I_1) = 411.0 mR/hr; distance 1 (d_1) = 3.6000 m; distance 2 (d_2) = 1.1000 m, determine the intensity at distance 2 (I_2) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_2 is given, so isolate I_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_2:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 411.0 mR/hr, distance 1 (d_1) = 3.6000 m, distance 2 (d_2) = 1.1000 m.

4. Step 4 — Substitute the given values:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{2} = 4402\ \text{mR/hr}$$

6. Step 6 — Check: returning I_2 = 4,402 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 8,804 — kept a factor of two that cancels in the correct rearrangement.
• 2,201 — dropped that same factor in the other direction.
• 4,842 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

inverse square law used to set a safe worker distance from a radioactive source Given distance 1 (d_1) = 1.9000 m; distance 2 (d_2) = 7.4000 m; intensity at distance 2 (I_2) = 505.8 mR/hr, determine the intensity at distance 1 (I_1) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_1 is given, so isolate I_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_1:

   $$I_{1} = I_2\left(\dfrac{d_2}{d_1}\right)^2$$

3. Step 3 — List the givens: distance 1 (d_1) = 1.9000 m, distance 2 (d_2) = 7.4000 m, intensity at distance 2 (I_2) = 505.8 mR/hr.

4. Step 4 — Substitute the given values:

   $$I_{1} = I_2\left(\dfrac{d_2}{d_1}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{1} = 7673\ \text{mR/hr}$$

6. Step 6 — Check: returning I_1 = 7,673 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 15,345 — kept a factor of two that cancels in the correct rearrangement.
• 3,836 — dropped that same factor in the other direction.
• 8,440 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

radiation shielding distance calculated with the inverse square law Given intensity at distance 1 (I_1) = 922.0 mR/hr; distance 1 (d_1) = 0.8000 m; intensity at distance 2 (I_2) = 83.7050 mR/hr, determine the distance 2 (d_2) in m.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except d_2 is given, so isolate d_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for d_2:

   $$d_{2} = d_1\sqrt{\dfrac{I_1}{I_2}}$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 922.0 mR/hr, distance 1 (d_1) = 0.8000 m, intensity at distance 2 (I_2) = 83.7050 mR/hr.

4. Step 4 — Substitute the given values:

   $$d_{2} = d_1\sqrt{\dfrac{I_1}{I_2}}$$

5. Step 5 — Evaluate:

   $$d_{2} = 2.6551\ \text{m}$$

6. Step 6 — Check: returning d_2 = 2.6551 m to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5.3102 — kept a factor of two that cancels in the correct rearrangement.
• 1.3275 — dropped that same factor in the other direction.
• 2.9206 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

inverse square law applied to radiation intensity from a point source Given intensity at distance 1 (I_1) = 745.0 mR/hr; distance 1 (d_1) = 1.1000 m; distance 2 (d_2) = 14.9000 m, determine the intensity at distance 2 (I_2) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_2 is given, so isolate I_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_2:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 745.0 mR/hr, distance 1 (d_1) = 1.1000 m, distance 2 (d_2) = 14.9000 m.

4. Step 4 — Substitute the given values:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{2} = 4.0604\ \text{mR/hr}$$

6. Step 6 — Check: returning I_2 = 4.0604 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 8.1208 — kept a factor of two that cancels in the correct rearrangement.
• 2.0302 — dropped that same factor in the other direction.
• 4.4664 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

inverse square law used to set a safe worker distance from a radioactive source Given distance 1 (d_1) = 2.0000 m; distance 2 (d_2) = 14.6000 m; intensity at distance 2 (I_2) = 360.7 mR/hr, determine the intensity at distance 1 (I_1) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_1 is given, so isolate I_1 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_1:

   $$I_{1} = I_2\left(\dfrac{d_2}{d_1}\right)^2$$

3. Step 3 — List the givens: distance 1 (d_1) = 2.0000 m, distance 2 (d_2) = 14.6000 m, intensity at distance 2 (I_2) = 360.7 mR/hr.

4. Step 4 — Substitute the given values:

   $$I_{1} = I_2\left(\dfrac{d_2}{d_1}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{1} = 19220\ \text{mR/hr}$$

6. Step 6 — Check: returning I_1 = 19,220 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 38,440 — kept a factor of two that cancels in the correct rearrangement.
• 9,610 — dropped that same factor in the other direction.
• 21,142 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

radiation shielding distance calculated with the inverse square law Given intensity at distance 1 (I_1) = 402.0 mR/hr; distance 1 (d_1) = 4.5000 m; intensity at distance 2 (I_2) = 305.2 mR/hr, determine the distance 2 (d_2) in m.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except d_2 is given, so isolate d_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for d_2:

   $$d_{2} = d_1\sqrt{\dfrac{I_1}{I_2}}$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 402.0 mR/hr, distance 1 (d_1) = 4.5000 m, intensity at distance 2 (I_2) = 305.2 mR/hr.

4. Step 4 — Substitute the given values:

   $$d_{2} = d_1\sqrt{\dfrac{I_1}{I_2}}$$

5. Step 5 — Evaluate:

   $$d_{2} = 5.1644\ \text{m}$$

6. Step 6 — Check: returning d_2 = 5.1644 m to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 10.3287 — kept a factor of two that cancels in the correct rearrangement.
• 2.5822 — dropped that same factor in the other direction.
• 5.6808 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law

inverse square law applied to radiation intensity from a point source Given intensity at distance 1 (I_1) = 957.0 mR/hr; distance 1 (d_1) = 3.7000 m; distance 2 (d_2) = 19.5000 m, determine the intensity at distance 2 (I_2) in mR/hr.

Start with the thinking

• The governing relation printed in this handbook section is Inverse Square Law.
• Everything except I_2 is given, so isolate I_2 symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• The inverse square law for radiation intensity relates source intensity to distance from a point radioactive source.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

2. Step 2 — Rearrange symbolically for I_2:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

3. Step 3 — List the givens: intensity at distance 1 (I_1) = 957.0 mR/hr, distance 1 (d_1) = 3.7000 m, distance 2 (d_2) = 19.5000 m.

4. Step 4 — Substitute the given values:

   $$I_{2} = I_1\left(\dfrac{d_1}{d_2}\right)^2$$

5. Step 5 — Evaluate:

   $$I_{2} = 34.4545\ \text{mR/hr}$$

6. Step 6 — Check: returning I_2 = 34.4545 mR/hr to

   $$I_2 = I_1 \left(\dfrac{d_1}{d_2}\right)^2$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 68.9090 — kept a factor of two that cancels in the correct rearrangement.
• 17.2273 — dropped that same factor in the other direction.
• 37.9000 — rounded an intermediate value before the final step.

Reference: FE Handbook — Inverse Square Law