The mass of an electron is `9.1xx10^(-31)` kg and velocity is `2.99xx10^(10) cm s^(-1)`. The wavelenth of the electron will be

Options

A. 0.243 `"Å"`
B. 0.0243 `"Å"`
C. 4.21 `"Å"`
D. 0.421 `"Å"`

Explanation

To find the wavelength of an electron given its mass and velocity, we can use the de Broglie wavelength formula:

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

Where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) Joule seconds),
- \(m\) is the mass of the electron (\(9.1 \times 10^{-31}\) kg),
- \(v\) is the velocity of the electron.

### Step-by-Step Solution:

**Step 1: Convert the velocity from cm/s to m/s.**
- Given velocity: \(v = 2.99 \times 10^{10} \, \text{cm/s}\)
- To convert to m/s, we use the conversion factor \(1 \, \text{cm} = 0.01 \, \text{m}\):
\[ v = 2.99 \times 10^{10} \, \text{cm/s} \times 0.01 \, \text{m/cm} = 2.99 \times 10^{8} \, \text{m/s} \]

**Step 2: Substitute the values into the de Broglie wavelength formula.**
- Using the values:
- \(h = 6.626 \times 10^{-34} \, \text{J s}\)
- \(m = 9.1 \times 10^{-31} \, \text{kg}\)
- \(v = 2.99 \times 10^{8} \, \text{m/s}\)

Substituting these values into the formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{(9.1 \times 10^{-31})(2.99 \times 10^{8})} \]

**Step 3: Calculate the denominator.**
- First, calculate \(m \cdot v\):
\[ m \cdot v = 9.1 \times 10^{-31} \, \text{kg} \times 2.99 \times 10^{8} \, \text{m/s} = 2.72 \times 10^{-22} \, \text{kg m/s} \]

**Step 4: Calculate the wavelength.**
- Now substitute back into the wavelength formula:
\[ \lambda = \frac{6.626 \times 10^{-34}}{2.72 \times 10^{-22}} \approx 2.44 \times 10^{-12} \, \text{m} \]

**Step 5: Convert the wavelength to angstroms.**
- Since \(1 \, \text{angstrom} = 10^{-10} \, \text{m}\):
\[ \lambda = 2.44 \times 10^{-12} \, \text{m} = 0.0244 \, \text{angstrom} \]

### Final Answer:
The wavelength of the electron is approximately \(0.0244 \, \text{angstrom}\).