In an agricultural expertiment, a solution containing 1 mole of a radioactive material (t1/2=14.3 days) aws injected into roots of a plant. the plant was allowed 70 hours to settle down and then activity was measured in its fruit. if the activity measured was 1micro Ci, what percent of activity is transmitted from the root to the fruit in steady state?

To determine the percentage of activity transmitted from the roots of the plant to its fruit, we first need to understand the decay of the radioactive material over time and how much of it remains after a certain period. In this case, we have a half-life (t1/2) of 14.3 days for the radioactive material, and we need to calculate how much of the original activity remains after 70 hours.

Calculating Remaining Activity

The first step is to convert the time from hours to days since the half-life is given in days. There are 24 hours in a day, so:

• 70 hours = 70 / 24 days ≈ 2.92 days

Next, we can use the formula for radioactive decay, which is:

A = A0 * (1/2)^(t/t1/2)

Where:

• A = remaining activity
• A0 = initial activity
• t = time elapsed
• t1/2 = half-life

In this scenario, we start with 1 mole of the radioactive material. Assuming the initial activity (A0) is proportional to the amount of radioactive material, we can set A0 to 1 microcurie (µCi) for simplicity. Now we can plug in the values:

A = 1 µCi * (1/2)^(2.92 days / 14.3 days)

Calculating the Exponent

Now, we calculate the exponent:

• 2.92 / 14.3 ≈ 0.204

Now we can calculate the remaining activity:

A ≈ 1 µCi * (1/2)^(0.204)

Using a calculator, we find:

• (1/2)^(0.204) ≈ 0.870

Thus, the remaining activity is:

A ≈ 1 µCi * 0.870 ≈ 0.870 µCi

Calculating the Percentage of Activity Transmitted

Now that we know the remaining activity in the roots after 70 hours is approximately 0.870 µCi, we can find the percentage of this activity that is measured in the fruit. The activity measured in the fruit is given as 1 µCi. To find the percentage of activity transmitted from the roots to the fruit, we can use the formula:

Percentage = (Activity in fruit / Remaining activity in roots) * 100

Substituting the values:

Percentage = (1 µCi / 0.870 µCi) * 100

Calculating this gives:

• Percentage ≈ 1.149 * 100 ≈ 114.9%

Interpreting the Result

A percentage greater than 100% indicates that the activity measured in the fruit exceeds the remaining activity in the roots. This could suggest that the plant has effectively concentrated the radioactive material in its fruit, or there may be other factors at play, such as measurement errors or additional sources of activity.

In summary, the percentage of activity transmitted from the roots to the fruit is approximately 114.9%, indicating a significant transfer and concentration of the radioactive material in the fruit.