For a radioactive material, its activity `A` and rate of change of its activity of `R` are defined as `A=(-dN)/(dt)` and `R=(-dA)/(dt)`, where `N(t)` is the number of nuclei at time `t`. Two radioactive source `P` (mean life `tau`) and `Q` (mean life `2 tau`) have the same activity at `t=0`. Their rates of activities at `t=2 tau` are `R_(p)` and `R_(Q)`, respectively. If `(R_(P))/(R_(Q))=(n)/(e )`, then the value of `n` is:

Explanation

To solve the problem, we need to analyze the activities and rates of change of activities for the two radioactive sources, P and Q, using the definitions provided.

### Step-by-Step Solution:

1. **Define the Initial Conditions**:
- Let the initial activity of both sources at time \( t = 0 \) be \( A_0 \).

2. **Activity of Source P**:
- The activity \( A_P(t) \) of source P at time \( t \) is given by:
\[ A_P(t) = A_0 e^{-t/\tau} \]

3. **Activity of Source Q**:
- The activity \( A_Q(t) \) of source Q at time \( t \) is given by:
\[ A_Q(t) = A_0 e^{-t/(2\tau)} \]

4. **Rate of Change of Activity for Source P**:
- The rate of change of activity \( R_P \) for source P is:
\[ R_P = -\frac{dA_P}{dt} = -\frac{d}{dt}(A_0 e^{-t/\tau}) = \frac{A_0}{\tau} e^{-t/\tau} \]

5. **Rate of Change of Activity for Source Q**:
- The rate of change of activity \( R_Q \) for source Q is:
\[ R_Q = -\frac{dA_Q}{dt} = -\frac{d}{dt}(A_0 e^{-t/(2\tau)}) = \frac{A_0}{2\tau} e^{-t/(2\tau)} \]

6. **Evaluate Rates at \( t = 2\tau \)**:
- Substitute \( t = 2\tau \) into the expressions for \( R_P \) and \( R_Q \):
\[ R_P(2\tau) = \frac{A_0}{\tau} e^{-2\tau/\tau} = \frac{A_0}{\tau} e^{-2} \]
\[ R_Q(2\tau) = \frac{A_0}{2\tau} e^{-2\tau/(2\tau)} = \frac{A_0}{2\tau} e^{-1} \]

7. **Calculate the Ratio of Rates**:
- Now, we find the ratio \( \frac{R_P}{R_Q} \):
\[ \frac{R_P}{R_Q} = \frac{\frac{A_0}{\tau} e^{-2}}{\frac{A_0}{2\tau} e^{-1}} = \frac{2 e^{-2}}{e^{-1}} = 2 e^{-1} \]

8. **Relate the Ratio to Given Expression**:
- We are given that:
\[ \frac{R_P}{R_Q} = \frac{n}{e} \]
- Setting the two expressions equal gives:
\[ 2 e^{-1} = \frac{n}{e} \]

9. **Solve for \( n \)**:
- Multiply both sides by \( e \):
\[ 2 = n \]

### Final Answer:
The value of \( n \) is \( 2 \).