The isotope samarium-151 decays into europium-151, with a half-life of around 96.6 years. A rock contains 5 grams of samarium-151 when it reaches its closure temperature, and it contains 0.625 grams when it is discovered. The time since the rock reached its closure temperature is

years. When the rock was discovered, it had

grams of europium-151.

See explanation

Step-by-step explanation:

Mass of  samarium-151  originally present (No) = 5 g

Mass of  samarium-151 discovered (N) = 0.625 grams

time taken = ?

half life of samarium-151 (t1/2) = 96.6 years

From

N/No = (1/2)^t/t1/2

0.625/5 = (1/2)^t/96

0.125 = (1/2)^t/96

1/8 = (1/2)^t/96

(1/2)^3 = (1/2)^t/96

3 = t/96

t = 3 * 96

t = 288 years

The mass of europium-151 when the rock was discovered is obtained from;

Fraction of  samarium-151  left = 1/8

Fraction of  europium-151 formed = 1 - 1/8 = 7/8

Mass of  europium-151 = 7/8 * 5 = 4.375 g

probability for j is 1/4

while

a is 1/6