A certain nuclide has a half-life period of 30 minutes. If a sample containing 600 atoms is allowed to decay for 90 minutes, how many atoms will remain.

Options

A. 200 atoms
B. 450 atoms
C. 75 atoms
D. 500 atoms

Answer

To solve the problem of how many atoms will remain after a certain period of decay, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Half-Life**:
The half-life of the nuclide is given as 30 minutes.

2. **Determine the Total Decay Time**:
The sample is allowed to decay for 90 minutes.

3. **Calculate the Number of Half-Lives**:
To find out how many half-lives fit into the total decay time, we divide the total decay time by the half-life:
\[ \text{Number of half-lives} = \frac{\text{Total decay time}}{\text{Half-life}} = \frac{90 \text{ minutes}}{30 \text{ minutes}} = 3 \]
This means that 3 half-lives have occurred.

4. **Calculate the Remaining Atoms**:
We start with 600 atoms. After each half-life, the number of atoms is halved. We can calculate the remaining atoms after each half-life:
- After 1st half-life (30 minutes):
\[ 600 \div 2 = 300 \text{ atoms} \]
- After 2nd half-life (60 minutes):
\[ 300 \div 2 = 150 \text{ atoms} \]
- After 3rd half-life (90 minutes):
\[ 150 \div 2 = 75 \text{ atoms} \]

5. **Final Result**:
Therefore, after 90 minutes, the number of remaining atoms is 75.

### Summary:
After allowing the sample to decay for 90 minutes, 75 atoms will remain.

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