Thallium -208 has a half-life of 3.053 min. How long will it take for 120g t decat ot 7.50g

Well, if I were Thallium-208, I'd have a tough time deciding whether to decay or not. But let's calculate it anyway!

Given that the half-life of Thallium-208 is 3.053 minutes, we can use the equation for radioactive decay to figure out the time it takes for 120g to decay to 7.50g.

First, we need to find out how many half-lives it takes. Each half-life, the amount of Thallium-208 decreases by half.

Let's start with 120g and keep dividing by 2 until we reach 7.50g:

120g → 60g → 30g → 15g → 7.50g

It took us 4 half-lives to go from 120g to 7.50g.

Since each half-life is 3.053 minutes long, we multiply 4 by 3.053 minutes to get the total time it takes:

4 half-lives × 3.053 minutes per half-life = 12.212 minutes

So, it will take approximately 12.212 minutes for 120g of Thallium-208 to decay to 7.50g. Just enough time to tell a few jokes!

To calculate how long it will take for 120g of thallium-208 to decay to 7.50g, we can use the half-life of thallium-208.

The half-life of thallium-208 is given as 3.053 min.

We can use the half-life formula to find the number of half-lives it will take for the amount of thallium-208 to decrease from 120g to 7.50g.

Number of half-lives = (ln(N₀/Nₓ))/(ln(2))

Where:
N₀ = initial amount of thallium-208 (120g)
Nₓ = final amount of thallium-208 (7.50g)
ln = natural logarithm

Number of half-lives = (ln(120/7.50))/(ln(2))

Let's calculate the value of (ln(120/7.50))/(ln(2)):

Number of half-lives = (ln(16))/(ln(2))
Number of half-lives ≈ 4

So it will take approximately 4 half-lives for the amount of thallium-208 to decrease from 120g to 7.50g.

To find the total time it will take, we can multiply the half-life by the number of half-lives:

Total time = half-life × number of half-lives
Total time = 3.053 min × 4
Total time ≈ 12.212 min

Therefore, it will take approximately 12.212 minutes for 120g of thallium-208 to decay to 7.50g.

To determine how long it will take for 120g of thallium-208 to decay to 7.50g, we need to use the concept of half-life.

Here's the step-by-step explanation on how to solve this problem:

1. Determine the number of half-lives required to reach the desired amount of decay. This can be done by dividing the initial amount (120g) by the final amount (7.50g):
Number of half-lives = log(final amount / initial amount) / log(0.5)

Number of half-lives = log(7.50g / 120g) / log(0.5) [Using common logarithm]

2. Calculate the time required for the number of half-lives calculated in step 1. Multiply the number of half-lives by the half-life of thallium-208 (3.053 min):
Time required = Number of half-lives * half-life

Time required = (log(7.50g / 120g) / log(0.5)) * 3.053 min

By substituting the values into the formula, you can calculate the time required for the decay from 120g to 7.50g of thallium-208.

k = 0.693/t1/2

Substitute k into the equation below:
ln(No/N) = kt.
No = initial = 120g
N = final = 7.50g
k from above.
Solve for t.