Question

If the half-life of cesium-137 is 30 years, what is the approximate time required to reduce a 7kg sample to about 1g?

A) 60 years
B) 90 years
C) 120 years
D) 150 years

Answer 1

The approximate time required to reduce a 7kg sample of cesium-137 to about 1g is approximately 383.1 years.

Step-by-step explanation:

The half-life of cesium-137 is given as 30 years, and we want to know the approximate time required to reduce a 7kg sample to about 1g. We can use the concept of half-life to solve this problem.

Step 1: Determine the number of half-lives required to reduce the sample from 7kg to 1g.

Since each half-life reduces the sample size by half, we can calculate the number of half-lives as follows:

Number of half-lives = log2(initial mass/final mass)

Number of half-lives = log2(7000g/1g) = log2(7000) = 12.77 (approximately)

Step 2: Calculate the time required by multiplying the number of half-lives by the half-life:

Time required = Number of half-lives x Half-life = 12.77 x 30 years = 383.1 years (approximately)

Therefore, the approximate time required to reduce a 7kg sample of cesium-137 to about 1g is approximately 383.1 years.