The Speed of an electron having a wavelength of 9.0 cm is

Options

A. 0.0808`ms^(-1)`
B. 0.0121`ms^(-1)`
C. 0.821`ms^(-1)`
D. 81.21`ms^(-1)`

Answer

To find the speed of an electron having a wavelength of 9.0 cm, we can use the de Broglie wavelength formula. Here’s the step-by-step solution:

### Step 1: Convert Wavelength to Meters
The given wavelength (λ) is 9.0 cm. We need to convert this into meters for our calculations.

\[ \text{Wavelength in meters} = 9.0 \, \text{cm} \times \frac{1 \, \text{m}}{100 \, \text{cm}} = 0.09 \, \text{m} \]

**Hint:** Always convert units to the standard SI units before performing calculations.

### Step 2: Use the de Broglie Wavelength Formula
The de Broglie wavelength formula is given by:

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

Where:
- \( \lambda \) = wavelength
- \( h \) = Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\))
- \( m \) = mass of the electron (\(9.1 \times 10^{-31} \, \text{kg}\))
- \( v \) = speed of the electron

### Step 3: Rearrange the Formula to Solve for Speed (v)
We can rearrange the formula to solve for the speed (v):

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

### Step 4: Substitute the Values
Now we can substitute the values into the formula:

\[ v = \frac{6.626 \times 10^{-34} \, \text{Js}}{(9.1 \times 10^{-31} \, \text{kg})(0.09 \, \text{m})} \]

### Step 5: Calculate the Speed
Now, we perform the calculation:

1. Calculate the denominator:

\[ 9.1 \times 10^{-31} \, \text{kg} \times 0.09 \, \text{m} = 8.19 \times 10^{-32} \, \text{kg m} \]

2. Now calculate the speed:

\[ v = \frac{6.626 \times 10^{-34}}{8.19 \times 10^{-32}} \approx 0.00808 \, \text{m/s} \]

### Final Answer
The speed of the electron is approximately:

\[ v \approx 0.00808 \, \text{m/s} \]

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