Y grams of a radioactive isotope take 120days to decay to 3.5grams. The half-life period of the isotope is 20 days
(a) Find the initial mass of the isotope
(b) Give one application of radioactivity in agriculture
Guide On Rating System
Vote
(a) To find the initial mass of the isotope, we can use the formula for exponential decay:
N(t) = N(0) * (1/2)^(t/T)
where:
N(t) is the final mass (3.5 grams),
N(0) is the initial mass (what we're trying to find),
t is the time elapsed (120 days), and
T is the half-life period (20 days).
Plugging in the given values into the formula, we get:
3.5 = N(0) * (1/2)^(120/20)
Simplifying, we have:
3.5 = N(0) * (1/2)^6
Since (1/2)^6 is equal to 1/64, we can rewrite the equation as:
3.5 = N(0) / 64
Multiplying both sides by 64, we find:
N(0) = 3.5 * 64
N(0) = 224 grams
Therefore, the initial mass of the isotope is 224 grams.
(b) One application of radioactivity in agriculture is the use of radiation for pest control. Gamma rays and X-rays can be used to sterilize pests, such as insects and agricultural pathogens, without damaging the crops or the environment. This method, known as sterile insect technique (SIT), involves exposing the pests to radiation, rendering them infertile so they cannot reproduce and cause damage to crops. This technique can reduce or eliminate the need for chemical pesticides and is widely used in the agricultural industry to protect crops and increase yields.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99