notesonly.in

Problem: Calculate the de Broglie wavelength of an electron moving with a velocity of 2.0 x 10^6 m/s. Given: mass of electron (m) = 9.11 x 10^-31 kg, Planck's constant (h) = 6.626 x 10^-34 J.s. Step 1: Identify the formula for de Broglie wavelength. λ = h / (m * v) Step 2: Substitute the given values into the formula. λ = 6.626 x 10^-34 / (9.11 x 10^-31 * 2.0 x 10^6) Step 3: Calculate the denominator. m * v = 9.11 x 10^-31 * 2.0 x 10^6 = 18.22 x 10^-25 kg.m/s Step 4: Divide h by the denominator. λ = 6.626 x 10^-34 / 18.22 x 10^-25 λ ≈ 0.3636 x 10^-9 m Step 5: Convert to standard form. λ ≈ 3.64 x 10^-10 m or 0.364 nm. This wavelength is comparable to the size of atoms, which is why wave nature is significant in atomic physics.