The speed of electron having de Broglie wavelength of` 10 ^(10)` m is
( me = `9.1 xx 10 ^(-31)` kg, h =` 6.63xx 10^(-34)` J-s)

Options

A. `7.28 xx 10 ^(6)` m/s
B. `4 xx 10^(6)` m/s
C. `8 xx10 ^(5)` m/s
D. `5.25 xx 10 ^(5)` m/s

Answer

To find the speed of an electron with a given de Broglie wavelength, we can use the de Broglie wavelength formula:

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

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

Given:
- \(\lambda = 10^{-10} \, \text{m}\) (corrected from \(10^{10}\)),
- \(h = 6.63 \times 10^{-34} \, \text{J-s}\),
- \(m = 9.1 \times 10^{-31} \, \text{kg}\).

We need to rearrange the formula to solve for \(v\):

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

Now, we can substitute the known values into the equation:

1. Substitute \(h\), \(m\), and \(\lambda\):

\[ v = \frac{6.63 \times 10^{-34}}{(9.1 \times 10^{-31})(10^{-10})} \]

2. Calculate the denominator:

\[ 9.1 \times 10^{-31} \times 10^{-10} = 9.1 \times 10^{-41} \]

3. Now substitute this back into the equation for \(v\):

\[ v = \frac{6.63 \times 10^{-34}}{9.1 \times 10^{-41}} \]

4. Perform the division:

\[ v = 7.28 \times 10^{6} \, \text{m/s} \]

Thus, the speed of the electron is:

\[ \boxed{7.28 \times 10^{6} \, \text{m/s}} \]