How long will it take for 15/16 of a radium isotope to decay?

How long will it take for 15/16 of a radium isotope to decay?

• A. 1,600 years
• B. 3,200 years
• C. 4,800 years
• D. 6,400 years

Answer: (D)

To determine how long it will take for 15/16 of a radium isotope to decay, we first need to understand the concept of half-life, which is the time it takes for half of the radioactive substance to decay. Each half-life reduces the amount of the substance in a specific way. If we start with 1 unit of the isotope, after one half-life, we would have 1/2 remaining; after two half-lives, we would have 1/4 remaining; after three half-lives, we would have 1/8 remaining; and after four half-lives, we would have 1/16 remaining. To find the time it takes for 15/16 of the isotope to decay, we can calculate how many half-lives it takes to get from the original amount (1) to the remaining amount (1/16). Since 15/16 of the isotope has decayed, only 1/16 is left. From the sequence: - After 0 half-lives: 1 (100% remains) - After 1 half-life: 1/2 (50% remains) - After 2 half-lives: 1/4 (25% remains) -

To determine how long it will take for 15/16 of a radium isotope to decay, we first need to understand the concept of half-life, which is the time it takes for half of the radioactive substance to decay.

Each half-life reduces the amount of the substance in a specific way. If we start with 1 unit of the isotope, after one half-life, we would have 1/2 remaining; after two half-lives, we would have 1/4 remaining; after three half-lives, we would have 1/8 remaining; and after four half-lives, we would have 1/16 remaining.

To find the time it takes for 15/16 of the isotope to decay, we can calculate how many half-lives it takes to get from the original amount (1) to the remaining amount (1/16). Since 15/16 of the isotope has decayed, only 1/16 is left.

From the sequence:

• After 0 half-lives: 1 (100% remains)

• After 1 half-life: 1/2 (50% remains)

• After 2 half-lives: 1/4 (25% remains)