In the Davisson–Germer experiment, electrons accelerated through 54 V produce maximum scattering intensity at diffraction angle 50° using nickel. Their de Broglie wavelength is approximately 0.8N, where N is an integer. Find N. [The original source omits the unit following 0.8N.]
Physics · Mixed Chapter
JEE Mains

Question

In the Davisson–Germer experiment, electrons accelerated through 54 V produce maximum scattering intensity at diffraction angle 50° using nickel. Their de Broglie wavelength is approximately 0.8N, where N is an integer. Find N. [The original source omits the unit following 0.8N.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — An electron accelerated through potential V gains kinetic energy: (1/2)mv² = eV. Step 2 — Its momentum is p = √(2meV). By the de Broglie relation, λ = h/p. Step 3 — Expressing wavelength in ångströms for electrons, λ(Å) = 12.27/√V, with V in volts. Step 4 — At V = 54 V, λ = 12.27/√54 Å ≈ 1.67 Å. Step 5 — Compare the numerical coefficient with 0.8N: 0.8N ≈ 1.67 ⇒ N ≈ 2.09. Nearest integer N = 2 (printed key). Answer: 2. Source caution: The PDF prints “0.8N” without a wavelength unit. Th…