A particular radioactive substance has a half-life of 4 minutes. How long will it take for 250 g of this radioactive material to decay to less than 0.1g?

24 min
36 min
40 min
48 min
72 min

I got 32 min but that not one of the choices. Please help

How many half lives does it go through to get from 250 g to < 0.1g?

# half lives x 4 min = ?

To solve this problem, we need to use the half-life formula for radioactive decay. The formula is as follows:

N = N₀ * (1/2)^(t/t₁/₂)

Where:
N = Final amount of radioactive substance
N₀ = Initial amount of radioactive substance
t = Time elapsed
t₁/₂ = Half-life of the substance

In this case, the initial amount is 250 g, and we want to find the time it takes for the substance to decay to less than 0.1 g. So, we set up the equation as follows:

0.1 = 250 * (1/2)^(t/4)

To solve for t, we can take the logarithm of both sides:

log(0.1) = log(250 * (1/2)^(t/4))

log(0.1) = log(250) + (t/4) * log(1/2)

Now, we can solve for t using a scientific calculator or logarithm tables.

Taking logarithm base 10:

log(0.1) ≈ -1
log(250) ≈ 2.39794
log(1/2) ≈ -0.30103

Substituting these values back into the equation:

-1 = 2.39794 + (t/4) * -0.30103

-1 - 2.39794 = (t/4) * -0.30103

-3.39794 = (t/4) * -0.30103

Now, we can isolate t by multiplying both sides by -4:

-3.39794 * -4 = t * -0.30103

13.59176 = t * -0.30103

Finally, dividing both sides by -0.30103:

t = 13.59176 / -0.30103
t ≈ 45.12

So, it takes approximately 45.12 minutes for 250 g of the radioactive material to decay to less than 0.1 g.

None of the given options matches exactly, but the closest option is 48 min.