plutonium-239 is a radioactive isotope commonly used as fuel in nuclear reactors. the half-life of plutonium-239 is 24,100 years. about how long would it take 504 grams of plutonium-239 to decay until there were only 63 grams plutonium-239 left?

72,300 years.

Explanation:

What's the ratio between the current and the initial mass of this sample? In other words, what fraction of the initial sample hasn't yet decayed?

.

The value of this fraction starts at 1 decreases to 1/2 of its initial value after every half-life. How many times shall 1/2 be multiplied to 1 before reaching 1/8? . It takes three half-lives or years to reach that value.

In certain questions the denominator of the fraction is large. It might not even be an integer power of 2. The base-x logarithm function on calculators could help. Evaluate

to find the number of half-lives required. In case the base-x logarithm function isn't available, but the natural logarithm function is, apply the following expression (derived from the base-changing formula) to get the same result:

.

72,300 years.

Explanation:

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s