The velocity of an electron having wavelenth of 0.15 nm will be

Options

A. `4.85 xx10^(8) cm S^(-1)`
B. `2.84 xx10^(5) cm s^(-1)`
C. `2.07 xx10^(6) cm s^(-1)`
D. `1.312 xx10^(7) cm s^(-1)`

Answer

To find the velocity of an electron with a wavelength of 0.15 nm, we can use the de Broglie wavelength formula:

\[ \lambda = \frac{h}{mv} \]

Where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant,
- \(m\) is the mass of the electron,
- \(v\) is the velocity of the electron.

### Step-by-Step Solution:

**Step 1: Convert Wavelength to Centimeters**
The given wavelength is in nanometers. We need to convert it to centimeters for consistency in units.

\[ \lambda = 0.15 \, \text{nm} = 0.15 \times 10^{-7} \, \text{cm} \]

**Step 2: Write Down Known Values**
- Planck's constant (\(h\)) in CGS units:
\[ h = 6.626 \times 10^{-27} \, \text{cm}^2 \, \text{g/s} \]
- Mass of the electron (\(m\)) in CGS units:
\[ m = 9.1 \times 10^{-28} \, \text{g} \]

**Step 3: Rearrange the de Broglie Equation to Solve for Velocity**
From the de Broglie equation, we can rearrange it to find \(v\):

\[ v = \frac{h}{m\lambda} \]

**Step 4: Substitute the Values into the Equation**
Now, substitute the known values into the rearranged equation:

\[ v = \frac{6.626 \times 10^{-27}}{9.1 \times 10^{-28} \times 0.15 \times 10^{-7}} \]

**Step 5: Calculate the Velocity**
Now, perform the calculation:

1. Calculate the denominator:
\[ 9.1 \times 10^{-28} \times 0.15 \times 10^{-7} = 1.365 \times 10^{-35} \]

2. Now divide \(h\) by the result:
\[ v = \frac{6.626 \times 10^{-27}}{1.365 \times 10^{-35}} \approx 4.85 \times 10^{8} \, \text{cm/s} \]

### Final Answer:
The velocity of the electron having a wavelength of 0.15 nm is approximately:

\[ v \approx 4.85 \times 10^{8} \, \text{cm/s} \]