Question

What is the wavelength associated with an electron moving with a velocity of \(10^6 \, \text{m/s}\)?
(\(h = 6.63 \times 10^{-34} \, \text{Js}\))

• A. 72.7 nm
• B. 7.27 nm
• C. 0.727 nm
• D. 0.0727 nm

Hint:

Electron wavelengths are typically in nanometer range for such speeds.

Answer 1

The Correct Option is C

Concept: De Broglie wavelength: \[ \lambda = \frac{h}{mv} \]

Step 1: Substitute values.
\[ m = 9.1 \times 10^{-31} \, \text{kg}, \quad v = 10^6 \] \[ \lambda = \frac{6.63 \times 10^{-34}}{9.1 \times 10^{-31} \times 10^6} \]

Step 2: Simplify.
\[ \lambda = \frac{6.63}{9.1} \times 10^{-9} = 0.727 \times 10^{-9} \, \text{m} \] \[ \lambda = 0.727 \, \text{nm} \]