The mass to charge ratio `(m//e)` for a cation `1.5xx10^(-8)` `kg//C.` What is the mass of this cation?

Options

A. (a) `2.4xx10^(-19)` g
B. (b) `2.4xx10^(-27)` g
C. (c) `2.4xx10^(-24)`g
D. (d) None of these

Answer

To solve the problem of finding the mass of the cation given its mass to charge ratio, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
We are given the mass to charge ratio `(m/e)` for a cation, which is `1.5 x 10^(-8) kg/C`.

2. **Identify the Charge of the Cation**:
The charge of a cation can be assumed to be the same as the charge of an electron, which is approximately `1.6 x 10^(-19) C`.

3. **Set Up the Equation**:
The mass to charge ratio can be expressed as:
\[ \frac{m}{e} = 1.5 \times 10^{-8} \text{ kg/C} \]
where `m` is the mass of the cation and `e` is the charge.

4. **Rearranging the Equation**:
To find the mass `m`, we can rearrange the equation:
\[ m = (m/e) \times e \]
Substituting the known values:
\[ m = (1.5 \times 10^{-8} \text{ kg/C}) \times (1.6 \times 10^{-19} \text{ C}) \]

5. **Perform the Calculation**:
Now, calculate the mass:
\[ m = 1.5 \times 1.6 \times 10^{-8} \times 10^{-19} \]
\[ m = 2.4 \times 10^{-27} \text{ kg} \]

6. **Convert the Mass to Grams**:
Since the mass is given in kilograms and we need it in grams, we use the conversion factor (1 kg = 1000 g):
\[ m = 2.4 \times 10^{-27} \text{ kg} \times 1000 \text{ g/kg} = 2.4 \times 10^{-24} \text{ g} \]

7. **Final Result**:
The mass of the cation is:
\[ 2.4 \times 10^{-24} \text{ g} \]