Question

What is the wavelength (in nm) of an electron moving at 1×10⁶ m/s?

A) 1.23 nm
B) 2.45 nm
C) 5.78 nm
D) 10.56 nm

Answer 1

The wavelength of an electron can be calculated using the de Broglie wavelength equation: λ = h/mv. Plugging in the given velocity, we find that the wavelength is approximately 7.26 × 10^-3 nm.

Step-by-step explanation:

To calculate the wavelength of an electron, we can use the de Broglie wavelength equation:

λ = h/mv

Where:

• λ is the wavelength
• h is Planck's constant (6.626 × 10^-34 J·s)
• m is the mass of the electron (9.11 × 10^-31 kg)
• v is the velocity of the electron

Plugging in the given velocity of 1 × 10^6 m/s, we can calculate the wavelength as follows:

λ = (6.626 × 10^-34 J·s) / (9.11 × 10^-31 kg) / (1 × 10^6 m/s)

Calculating this expression, we find that the wavelength is approximately 7.26 × 10^-3 nm. Therefore, none of the given answer choices are correct.