what should be the velocity of an electron so that its momentum becoumes equal to that of a photn of wavelength `5200 Å`

Options

A. 700 m/s
B. 1000 m/s
C. 1400 m/s
D. 2800 m/s

Explanation

To find the velocity of an electron such that its momentum is equal to that of a photon with a wavelength of 5200 Å, we can follow these steps:

### Step 1: Calculate the momentum of the photon
The momentum \( P \) of a photon can be calculated using the formula:
\[ P = \frac{h}{\lambda} \]
where:
- \( h \) is Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{Js} \)
- \( \lambda \) is the wavelength of the photon.

Given that the wavelength \( \lambda = 5200 \, \text{Å} = 5200 \times 10^{-10} \, \text{m} \), we can substitute these values into the equation.

### Step 2: Substitute the values
Substituting the values into the momentum formula:
\[ P = \frac{6.626 \times 10^{-34}}{5200 \times 10^{-10}} \]

### Step 3: Calculate the momentum of the photon
Now, calculate the value:
\[ P = \frac{6.626 \times 10^{-34}}{5.2 \times 10^{-7}} \approx 1.272 \times 10^{-27} \, \text{kg m/s} \]

### Step 4: Set the momentum of the electron equal to that of the photon
The momentum of the electron \( P_e \) can be expressed as:
\[ P_e = m_e \cdot v \]
where:
- \( m_e \) is the mass of the electron, \( m_e = 9.1 \times 10^{-31} \, \text{kg} \)
- \( v \) is the velocity of the electron.

Setting the momentum of the electron equal to the momentum of the photon:
\[ m_e \cdot v = P \]

### Step 5: Solve for the velocity \( v \)
Rearranging the equation to solve for \( v \):
\[ v = \frac{P}{m_e} \]
Substituting the values we calculated:
\[ v = \frac{1.272 \times 10^{-27}}{9.1 \times 10^{-31}} \approx 1.4 \times 10^{3} \, \text{m/s} \]

### Conclusion
Thus, the velocity of the electron should be approximately \( 1400 \, \text{m/s} \).