Question

If the initial amount of iridium-192 produces radiation at 1,000 times the safe level, how long will it take before radiation levels drop below the safe level? reddit

Answer 1

To cause death within hours of exposure to radiation, the dose needs to be very high, 10Gy or higher, while 4-5Gy will kill within 60 days, and less than 1.5-2Gy will not be lethal in the short term. However all doses, no matter how small, carry a finite risk of cancer and other diseases. Patients exposed to radiation between 8 to 30 Gy experience nausea and severe diarrhea within an hour, and they die between 2 days and 2 weeks after exposure. Absorbed doses greater than 30 Gy cause neurological damage

Answer 2

A radioactive isotope is a species of an element with the same and equal chemical element but posses varying mass numbers.

Iridium is a radioactive isotope with a half-life of 74 days.

i.e.

$\mathbf{ T_{1/2} = 74 \ days}$

Let assume that:

• the size of a radioactive element = N
• at a time = t

where;

• population reduction = dN
• at time = dt

∴

The rate of change can be expressed by the equation:

$\mathbf{\dfrac{dN}{dt}=-\lambda N}$----- (1)

Here:

λ = decay constant

By integrating equation (1) and making the decay constant the subject of the formula:

The formula for calculating the decay constant can be expressed as:

$\mathbf{\lambda = \dfrac{In{(2)}}{T_{1/2}}}$

$\mathbf{\lambda = \dfrac{0.693}{T_{1/2}}}$

$\mathbf{\lambda = \dfrac{0.693}{74}}$

$\mathbf{\lambda = 0.009365}$

Using the first-order reaction of chemical kinetics to determine the time required for Iridium to drop below the safety level, we have;

$\mathbf{t = (\dfrac{1}{k}) In (\dfrac{a}{a-x})}$

where;

a = initial amount of the radioisotope = 1000

a - x = final amount = 1

∴

$\mathbf{t = (\dfrac{1}{0.009365}) In (\dfrac{1000}{1})}$

t = 737.6 days

Therefore, we can conclude that the amount of time it requires iridium to drop below the safety level is =737.6 days

Learn more about chemical kinetics here:

https://brainly.com/question/13787506?referrer=searchResults