What is the value of decay constant of a compound having half life time of 2.95 days?

Options

A. `2.9 times 10^-5s^-1`
B. `2.9 times 10^6 s^-1`
C. `2.9 times 10^-6 s^-1`
D. `3 times 10^5 s^-1`

Answer

To find the decay constant (λ) of a compound given its half-life (T_half), we can use the formula for first-order reactions:

\[ \lambda = \frac{0.693}{T_{half}} \]

### Step-by-Step Solution:

**Step 1: Convert the half-life from days to seconds.**

Given:
- Half-life (T_half) = 2.95 days

To convert days into seconds:
- 1 day = 24 hours
- 1 hour = 3600 seconds

So,
\[ T_{half} = 2.95 \, \text{days} \times 24 \, \text{hours/day} \times 3600 \, \text{seconds/hour} \]

Calculating this:
\[ T_{half} = 2.95 \times 24 \times 3600 = 254880 \, \text{seconds} \]

**Step 2: Use the half-life to calculate the decay constant.**

Now, we can substitute T_half into the decay constant formula:
\[ \lambda = \frac{0.693}{T_{half}} = \frac{0.693}{254880} \]

Calculating this:
\[ \lambda \approx 2.71 \times 10^{-6} \, \text{per second} \]

**Step 3: Identify the closest answer option.**

From the calculated value, we see that:
\[ \lambda \approx 2.71 \times 10^{-6} \, \text{per second} \]
This is approximately equal to the option:
- 2.9 × 10^(-6) per second (Option 3)

### Final Answer:
The decay constant (λ) of the compound is approximately:
\[ \lambda \approx 2.9 \times 10^{-6} \, \text{per second} \]