After an electron has been accelerated through a potential difference of 0.15 kV,what is its de Broglie wavelength? (e = 1.60 × 10^-1⁹ C,m_electron = 9.11 × 10^-31 kg,h = 6.626 × 10^-34 J ∙ s) A)0.10 nm B)1.0 nm C)1.0 mm D)1.0 cm

Question

Quizplus · Accepted Answer

The equation for de Broglie wavelength is λ = h/p, where p is the momentum of the electron. The momentum of the electron can be calculated using the formula p = √(2mE), where m is the mass of the electron and E is the potential difference it has been accelerated through.

Here, m = 9.11 × 10^-31 kg, E = 0.15 kV = 0.15 × 10^3 V.

Using the formula, p = √(2mE) = √(2 × 9.11 × 10^-31 × 1.60 × 10^3) = 1.16 × 10^-24 kg m/s

Now, we can calculate the de Broglie wavelength using λ = h/p = 6.626 × 10^-34/(1.16 × 10^-24) = 5.7 × 10^-11 m = 0.057 nm

Therefore, the closest option is A) 0.10 nm.

After an Electron Has Been Accelerated Through a Potential Difference