What is the de Broglie wavelength of an electron (mass m = 9.11 10^-31 kg) accelerated from rest through a potential difference of 100 V (Planck constant h = 6.626 10^-34 J s, e = 1.602 * 10^-19 C)?
Answer and explanation
Correct answer: D. 0.123 nm
- Step 1: Kinetic energy: K = e V = 1.602 10^-17 J.
- Step 2: Momentum: p = sqrt(2 m K) = sqrt(2 9.11 10^-31 1.602 10^-17) = sqrt(2.919 10^-47) = 5.403 10^-24 kg m/s.
- Step 3: de Broglie wavelength: lambda = h / p = (6.626 10^-34) / (5.403 10^-24) = 1.226 * 10^-10 m = 0.123 nm.
Answer
0.123 nm.
Why not the others: 1.23 nm is off by a factor of 10 from unit conversion; 0.0123 nm corresponds to 10 kV acceleration; 0.246 nm uses 25 V.
Practise more Electromagnetism, Wave Optics and Modern Physics.
Free questions with an explanation for every one, and full timed Bagrut (Secondary School Matriculation) mock tests.
More Electromagnetism, Wave Optics and Modern Physics questions
- A 1.0 kg block attached to a horizontal spring oscillates with simple harmonic motion. When its displacement is x = 0.05 m, its speed is v =…
- Two identical spheres A and B undergo an elastic oblique collision in two dimensions. Sphere A is initially moving at speed v and sphere B i…
- What is the period of a simple pendulum of length L = 0.98 m in a location where g = 9.8 m/s^2 for small amplitude oscillations?
- A 0.1 kg bullet traveling horizontally at 400 m/s embeds into a 3.9 kg wooden block initially at rest on a frictionless table. What fraction…
- In a damped harmonic oscillator, the mechanical energy decreases by 10% in each full cycle. After 3 complete cycles, what percentage of the…
- A mass m suspended from a vertical spring oscillates with frequency f. If the spring is cut in half and the same mass m is suspended from on…