If wavelength is equal to the distance travelled by the electron in one second then

Options

A. `lambda = h//p`
B. `lambda = h//m`
C. `lambda = sqrt(h//p)`
D. `lambda = sqrt(h//m)`

Explanation

To solve the problem, we start with the given information that the wavelength (λ) is equal to the distance traveled by the electron in one second.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We know from de Broglie's hypothesis that the wavelength (λ) of a moving particle is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle.

2. **Momentum Definition**:
The momentum \( p \) of a particle can be expressed as:
\[ p = mv \]
where \( m \) is the mass of the particle and \( v \) is its velocity.

3. **Substituting Momentum into Wavelength Formula**:
Substituting the expression for momentum into the wavelength formula gives:
\[ \lambda = \frac{h}{mv} \]

4. **Distance Traveled by Electron**:
According to the problem, the distance traveled by the electron in one second is equal to the wavelength. Therefore, we can express this as:
\[ \text{Distance} = v = \lambda \]

5. **Setting Up the Equation**:
Since we have established that \( v = \lambda \), we can substitute this into our wavelength equation:
\[ \lambda = \frac{h}{m\lambda} \]

6. **Rearranging the Equation**:
To eliminate λ from the denominator, we multiply both sides by λ:
\[ \lambda^2 = \frac{h}{m} \]

7. **Solving for Wavelength**:
Taking the square root of both sides gives us:
\[ \lambda = \sqrt{\frac{h}{m}} \]

### Final Result:
Thus, the wavelength of the electron, given that it is equal to the distance traveled in one second, is:
\[ \lambda = \sqrt{\frac{h}{m}} \]