What will happen to the mass of electron if it travels with velocity of light ?

Options

A. `2m_(e )`
B. `3m_(e )`
C. infinite
D. zero

Answer

To solve the question "What will happen to the mass of an electron if it travels with the velocity of light?", we can follow these steps:

### Step 1: Understand the concept of mass in relativity
In the context of special relativity, the mass of an object increases as its velocity approaches the speed of light. The mass of an object in motion (m) is related to its rest mass (m₀) by the equation:

\[ m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} \]

where:
- \( m \) is the relativistic mass,
- \( m_0 \) is the rest mass,
- \( v \) is the velocity of the object,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

### Step 2: Set the velocity to the speed of light
In this case, we are interested in what happens when the velocity \( v \) of the electron approaches the speed of light \( c \). Therefore, we will substitute \( v = c \) into the equation.

### Step 3: Substitute and simplify
Substituting \( v = c \) into the equation gives:

\[ m = \frac{m_0}{\sqrt{1 - \frac{c^2}{c^2}}} \]

This simplifies to:

\[ m = \frac{m_0}{\sqrt{1 - 1}} \]

### Step 4: Analyze the denominator
The expression in the denominator becomes:

\[ \sqrt{1 - 1} = \sqrt{0} = 0 \]

Thus, we have:

\[ m = \frac{m_0}{0} \]

### Step 5: Conclusion
Since dividing by zero is undefined, this implies that the mass \( m \) approaches infinity. Therefore, we conclude that:

**The mass of the electron will become infinite if it were to travel at the speed of light.**

### Final Answer
The correct answer is that the mass of the electron will become infinite when it travels at the velocity of light.

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