If an electron is accelerated from rest through a potential difference of 100 V, what is its de Broglie wavelength? A) 2.55 × 10⁻⁹ m B) 1.23 × 10⁻¹⁰ m C) 0.529 × 10⁻¹⁰ m D) 8.67 × 10⁻⁹ m E) 1.20 × 10⁻¹⁵ m

Question

Quizplus · Accepted Answer

The de Broglie wavelength of an electron can be calculated using the formula:

λ = h/p

where λ is the de Broglie wavelength, h is the Planck's constant, and p is the momentum of the electron.

To find the momentum of the electron, we can use the formula:

p = √(2mE)

where m is the mass of the electron and E is the potential difference.

Substituting the values given in the question, we get:

p = √(2 * 9.1 × 10^-31 kg * 100 V) = 9.08 × 10^-25 kg m/s

Substituting the momentum value in the de Broglie wavelength formula, we get:

λ = h/p = 6.63 × 10^-34 J s / 9.08 × 10^-25 kg m/s = 1.23 × 10^-10 m

Therefore, the correct choice is B.

If an Electron Is Accelerated from Rest Through a Potential