Question

The half-life of radium is 1690 years. If 60 grams are present now, how much will be present in 710 years?

Answer 1

To find out how much radium will be left after 710 years, we apply the half-life decay formula using the initial amount of 60 grams and the known half-life of 1690 years, arriving at approximately 50.41 grams remaining.

Step-by-step explanation:

The question involves the concept of half-life in radioactive decay, which is a chemistry topic covered in high school. We are asked to calculate how much of a 60-gram sample of radium will remain after 710 years, given its half-life of 1690 years.

To solve this, we use the formula for exponential decay:

N = N_0 (1/2)^(t/T)

where:

• N is the remaining amount of substance,
• N_0 is the initial amount of substance (60 grams in this case),
• t is the time elapsed,
• T is the half-life of the substance.

Plugging in the given values:

N = 60 grams (1/2)^(710 years / 1690 years)

We find the ratio of 710/1690, which simplifies to about 0.42. This exponentiation will give us the fraction of the original amount that remains after 710 years.

After calculations, we find that approximately 50.41 grams of radium will remain after 710 years.

Answer 2

Using the half-life formula for exponential decay, it can be calculated that approximately 45.9 grams of a 60 gram sample of radium will remain after 710 years based on its half-life of 1690 years.

Step-by-step explanation:

The question revolves around the concept of half-life, which is a key concept in the field of Physics and Chemistry, particularly, nuclear chemistry. You are given that the half-life of radium is 1690 years and asked to calculate the amount remaining after 710 years when you start with a 60 gram sample. To solve this, you would use the formula for exponential decay:

N(t) = N_0 * (1/2)^(t/T)

where:

N(t) is the remaining amount of substance after time t,

N_0 is the original amount of the substance,

t is the time that has elapsed,

T is the half-life of the substance.

Plugging in the values:

N(710) = 60 * (1/2)^(710/1690)

To find the exponent, divide the elapsed time by the half-life:

(710/1690) ≈ 0.42

Then, raise 1/2 to this exponent:

(1/2)^0.42 ≈ 0.765

And multiply this by the original amount:

N(710) ≈ 60 * 0.765 ≈ 45.9 grams

So, after 710 years, approximately 45.9 grams of radium will remain from the original 60 grams.