Nucleus of a radioactive material can undergo beta decay with half life of 4 minutes. Suppose beta decay starts with 4096 nuclei at t = 0,the number of nuclei left after 20 minutes would bea)1024b)128c)512d)256Correct answer is option 'B'. Can you explain this answer?

Question

Answer

**Given:**
- Half-life of the radioactive material = 4 minutes
- Number of nuclei at t = 0 = 4096

**To find:**
- Number of nuclei left after 20 minutes

**Solution:**

To solve this problem, we can use the concept of radioactive decay and the exponential decay formula.

The exponential decay formula is given by:
N(t) = N₀ * (1/2)^(t/T)

Where:
- N(t) is the number of nuclei remaining at time t
- N₀ is the initial number of nuclei
- t is the time that has elapsed
- T is the half-life of the radioactive material

**Step 1:** Calculate the number of half-lives that have occurred in 20 minutes.

Number of half-lives = t / T = 20 / 4 = 5

**Step 2:** Substitute the values into the exponential decay formula.

N(t) = N₀ * (1/2)^(t/T)
N(t) = 4096 * (1/2)^(5)

**Step 3:** Simplify the expression.

N(t) = 4096 * (1/2)^5
N(t) = 4096 * (1/32)
N(t) = 128

Therefore, the number of nuclei left after 20 minutes is 128. Hence, the correct answer is option B.

Answer

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