Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.1 meters?

Question

Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.1 meters?

Answer 1

62.5 * (3 / 2.1)^2

Answer 2

To find the intensity at a distance of 2.1 meters, we can use the inverse square law formula.

The formula for inverse square law is:

I1 / I2 = (D2^2 / D1^2)

Where:
I1 = initial intensity (at distance D1)
I2 = final intensity (at distance D2)

Given that the initial intensity (at 3 meters) is 62.5 milliroentgens per hour, we have:

I1 = 62.5 milliroentgens per hour
D1 = 3 meters

We need to find the final intensity (at 2.1 meters):
I2 = ?
D2 = 2.1 meters

Using the formula mentioned earlier:

I1 / I2 = (D2^2 / D1^2)

Plugging in the values we know:

62.5 milliroentgens per hour / I2 = (2.1^2 / 3^2)

Simplifying further:

62.5 milliroentgens per hour / I2 = 4.41 / 9

Cross-multiplying:

9 * 62.5 milliroentgens per hour = 4.41 * I2

562.5 milliroentgens per hour = 4.41 * I2

Now, solving for I2:

I2 = 562.5 milliroentgens per hour / 4.41

Calculating the result:

I2 ≈ 127.6984 milliroentgens per hour

Therefore, the intensity at a distance of 2.1 meters is approximately 127.6984 milliroentgens per hour.

Answer 3

To find the intensity at a distance of 2.1 meters, we can use the inverse square law relationship. The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the radiation source.

Let's denote the intensity at 3 meters as I1 and the intensity at 2.1 meters as I2. We have the following relationship:

I1 ∝ 1/distance^2

where ∝ means "is proportional to."

Now, we can set up the proportion using the given information:

I1/62.5 milliroentgens per hour = 1/(3 meters)^2

Simplifying, we have:

I1/62.5 = 1/9

Now, we can solve for I1:

I1 = 62.5/9

Next, we can set up the proportion to find the intensity at 2.1 meters:

I1/I2 = (3 meters)^2/(2.1 meters)^2

Substituting the value of I1, we get:

62.5/9 / I2 = 9/2.1^2

Simplifying the equation, we have:

62.5/9 / I2 = 9/4.41

Cross-multiplying, we get:

(62.5/9) * (4.41/9) = 1/I2

Now, we can solve for I2:

I2 = (9 * 4.41) / (62.5/9)

Using a calculator, we find that:

I2 ≈ 0.489 milliroentgens per hour

Therefore, the intensity at a distance of 2.1 meters is approximately 0.489 milliroentgens per hour.

Radiation​ machines, used to treat​ tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3​ meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.1 ​meters?

62.5 * (3 / 2.1)^2

To find the intensity at a distance of 2.1 meters, we can use the inverse square law formula.

To find the intensity at a distance of 2.1 meters, we can use the inverse square law relationship. The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the radiation source.

Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.1 meters?