1. The initial number of atoms in a radioactive element is 6.0×10 to the 20 power and it's half life is 10hrs. Calculate the number of atoms which have decay in 30hrs

To determine the number of atoms that have decayed from a radioactive element over a period of 30 hours, we can use the concept of half-life. The half-life is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is 10 hours, and we start with an initial quantity of 6.0 × 10²⁰ atoms.

Understanding Half-Life

Half-life is a crucial concept in radioactive decay. It tells us how long it takes for half of the radioactive atoms to transform into a different element or isotope. After each half-life, the number of remaining radioactive atoms is halved.

Calculating the Number of Half-Lives

First, we need to find out how many half-lives fit into the 30-hour period:

• Time period = 30 hours
• Half-life = 10 hours
• Number of half-lives = 30 hours / 10 hours = 3

Finding Remaining Atoms

Now that we know there are 3 half-lives in 30 hours, we can calculate how many atoms remain after these half-lives:

• Initial number of atoms = 6.0 × 10²⁰
• After 1 half-life (10 hours): 6.0 × 10²⁰ / 2 = 3.0 × 10²⁰
• After 2 half-lives (20 hours): 3.0 × 10²⁰ / 2 = 1.5 × 10²⁰
• After 3 half-lives (30 hours): 1.5 × 10²⁰ / 2 = 0.75 × 10²⁰

Calculating Decayed Atoms

To find the number of atoms that have decayed, we subtract the remaining atoms from the initial amount:

• Remaining atoms after 30 hours = 0.75 × 10²⁰
• Decayed atoms = Initial atoms - Remaining atoms
• Decayed atoms = 6.0 × 10²⁰ - 0.75 × 10²⁰ = 5.25 × 10²⁰

Final Result

Therefore, the number of atoms that have decayed after 30 hours is 5.25 × 10²⁰ atoms.