The value of charge on the oil droplets experimentally observed were `-1.6 xx 10^(-19)` and `-4 xx 10^(-19)` coulomb. The value of the electronic charge, indicated by these results is

Options

A. `1.6 xx 10^(-19)`
B. `-2.4 xx 10^(-19)`
C. `-4xx 10^(-19)`
D. `-0.8xx 10^(-19)`

Explanation

To find the value of the electronic charge indicated by the observed charges on the oil droplets, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Charge Relationship**:
The charge (Q) on the oil droplets can be expressed in terms of the electronic charge (E) and an integer (N) as:
\[ Q = N \cdot E \]
where N is a whole number (1, 2, 3, ...).

2. **Given Charges**:
We have two observed charges:
- \( Q_1 = -1.6 \times 10^{-19} \) coulombs
- \( Q_2 = -4.0 \times 10^{-19} \) coulombs

3. **Analyzing \( Q_1 \)**:
For \( Q_1 \):
\[ -1.6 \times 10^{-19} = N_1 \cdot E \]
Rearranging gives:
\[ E = \frac{-1.6 \times 10^{-19}}{N_1} \]
If we assume \( N_1 = 1 \), then:
\[ E = -1.6 \times 10^{-19} \text{ coulombs} \]

4. **Analyzing \( Q_2 \)**:
For \( Q_2 \):
\[ -4.0 \times 10^{-19} = N_2 \cdot E \]
Rearranging gives:
\[ E = \frac{-4.0 \times 10^{-19}}{N_2} \]
If we substitute \( E = -1.6 \times 10^{-19} \) from the previous step:
\[ -4.0 \times 10^{-19} = N_2 \cdot (-1.6 \times 10^{-19}) \]
Dividing both sides by \(-1.6 \times 10^{-19}\):
\[ N_2 = \frac{-4.0 \times 10^{-19}}{-1.6 \times 10^{-19}} = 2.5 \]
Since \( N_2 \) must be an integer, this value is not valid.

5. **Finding Valid Integer N**:
We can check other potential values for \( E \) to find a valid integer \( N \).
- If we try \( E = -0.8 \times 10^{-19} \):
- For \( Q_1 \):
\[ N_1 = \frac{-1.6 \times 10^{-19}}{-0.8 \times 10^{-19}} = 2 \]
- For \( Q_2 \):
\[ N_2 = \frac{-4.0 \times 10^{-19}}{-0.8 \times 10^{-19}} = 5 \]
Both \( N_1 \) and \( N_2 \) are integers.

6. **Conclusion**:
The value of the electronic charge indicated by the observed results is:
\[ E = -0.8 \times 10^{-19} \text{ coulombs} \]

### Final Answer:
The electronic charge indicated by the results is \( -0.8 \times 10^{-19} \) coulombs.