What is the mass (m) of an electron?

Answer

To find the mass of an electron, we can use the relationship between the charge of an electron and the charge-to-mass ratio of an electron. Here’s a step-by-step solution:

### Step 1: Identify the charge of an electron
The charge of an electron (e) is known to be:
\[ e = 1.602 \times 10^{-19} \text{ coulombs} \]

### Step 2: Identify the charge-to-mass ratio of an electron
The charge-to-mass ratio (q/m) of an electron is given as:
\[ \frac{q}{m} = 1.76 \times 10^{8} \text{ coulombs/gram} \]

### Step 3: Rearrange the formula to find mass
We can rearrange the formula for charge-to-mass ratio to find the mass (m) of the electron:
\[ m = \frac{q}{\frac{q}{m}} \]
Substituting the known values:
\[ m = \frac{1.602 \times 10^{-19} \text{ C}}{1.76 \times 10^{8} \text{ C/g}} \]

### Step 4: Calculate the mass
Now, performing the calculation:
\[ m = \frac{1.602 \times 10^{-19}}{1.76 \times 10^{8}} \]
\[ m \approx 9.1 \times 10^{-28} \text{ grams} \]

### Step 5: Convert grams to kilograms
To convert grams to kilograms, we divide by 1000:
\[ m \approx 9.1 \times 10^{-28} \text{ grams} = 9.1 \times 10^{-31} \text{ kg} \]

### Final Answer
The mass of an electron is approximately:
\[ m \approx 9.1 \times 10^{-31} \text{ kg} \]

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