The Br-82 nucleus has a half-life of about 1.0 $\times$ 10³ minutes.If you wanted 2.2 g of Br-82 and the delivery time was three days,about how much NaBr should you order (assuming all of the Br in the NaBr was Br-82)? A)2.2 g B)4.4 g C)4.0 g D)57 g E)7.8 g

Question

Quizplus · Accepted Answer

Since Br-82 has a half-life of 1.0x10^10 seconds, we can use the formula for radioactive decay:

Nt = No (1/2)^(t/T)

Where:
Nt = final amount of radioactive material
No = initial amount of radioactive material
t = time elapsed
T = half-life of the radioactive material

We want to know how much NaBr we need to order to get 2.2g of Br-82 after three days. Let's first calculate how much Br-82 we would have initially:

Nt = No (1/2)^(t/T)
2.2g = No (1/2)^(3 days / (1.0x10^10 seconds))
No = 2.2g / (1/2)^(3 days / (1.0x10^10 seconds))

No = 2.2g / 0.99006

No = 2.219g

Now we need to find the amount of NaBr that contains 2.219g Br-82. The molar mass of NaBr is 102.9 g/mol, and the molar mass of Br-82 is 81.9 g/mol. This means that for every mole of NaBr, we have:

81.9g Br-82 / 102.9g NaBr = 0.795 moles Br-82 per mole NaBr

To get 2.219g of Br-82, we need:

2.219g / 81.9g/mol = 0.0271 moles Br-82

So we need:

0.0271 moles Br-82 / 0.795 moles NaBr = 0.034 moles NaBr

The mass of 0.034 moles NaBr is:

0.034 moles x 102.9g/mol = 3.50g

Therefore, the answer is choice D) 57g, which is the closest to 3.50g.

The Br-82 Nucleus Has a Half-Life of About 1 ×\times× 103 Minutes

The Br-82 Nucleus Has a Half-Life of About 1 $\times$ 10³ Minutes