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 with a given half-life (t_half), we can use the relationship between the two. Here’s a step-by-step solution:

### Step 1: Understand the relationship between half-life and decay constant
The decay constant (λ) is related to the half-life (t_half) by the formula:
\[ \lambda = \frac{0.693}{t_{half}} \]

### Step 2: Identify the given half-life
The half-life given in the problem is:
\[ t_{half} = 2.95 \text{ days} \]

### Step 3: Convert half-life from days to seconds
Since the decay constant is typically expressed in terms of seconds, we need to convert the half-life from days to seconds. We know that:
\[ 1 \text{ day} = 86400 \text{ seconds} \]
Thus,
\[ t_{half} = 2.95 \text{ days} \times 86400 \text{ seconds/day} = 254880 \text{ seconds} \]

### Step 4: Substitute the half-life into the decay constant formula
Now that we have the half-life in seconds, we can substitute it into the decay constant formula:
\[ \lambda = \frac{0.693}{254880 \text{ seconds}} \]

### Step 5: Calculate the decay constant
Now, we perform the calculation:
\[ \lambda \approx \frac{0.693}{254880} \approx 2.72 \times 10^{-6} \text{ s}^{-1} \]

### Final Answer
Thus, the decay constant (λ) for the compound with a half-life of 2.95 days is approximately:
\[ \lambda \approx 2.72 \times 10^{-6} \text{ s}^{-1} \]

---