The unit for radioactive constant is

Options

A. time
B. time `mol^(-1)`
C. `time^(-1)`
D. `mol time^(-1)`

Answer

To determine the unit for the radioactive constant, we can follow these steps:

### Step 1: Understand the Concept of Radioactive Decay
Radioactive decay refers to the process by which an unstable atomic nucleus loses energy by emitting radiation. The rate at which this decay occurs is characterized by the radioactive constant, often denoted by the symbol \( \lambda \).

### Step 2: Define the Rate of Disintegration
The rate of disintegration is defined as the number of disintegrations (or decays) that occur per unit time. It is commonly expressed in units such as disintegrations per second (dps).

### Step 3: Analyze the Units
Since the rate of disintegration is expressed in terms of disintegrations per second, we can write this as:
\[ \text{Rate of disintegration} = \frac{\text{Number of disintegrations}}{\text{Time}} \]
This implies that the unit of the radioactive constant \( \lambda \) must be inversely related to time.

### Step 4: Determine the Unit for the Radioactive Constant
From the analysis, we can conclude that the unit for the radioactive constant \( \lambda \) is:
\[ \text{Unit of } \lambda = \text{Time}^{-1} \]
This means that the radioactive constant has units of \( \text{s}^{-1} \) (per second).

### Conclusion
Thus, the unit for the radioactive constant is time inverse, or \( \text{s}^{-1} \).

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