An electron is moving such that its de Broglie wavelength is 550 nm. If the kinetic energy of the electron is x 10⁻²⁵ J, the value of x is ________. (Given: mass of electron = 9 10⁻³¹ kg, h = 6.6 10⁻³⁴ Js)

Step-by-step solution

Given: de Broglie wavelength = 550 nm = 5.5 10⁻⁷ m Mass of electron m = 9 10⁻³¹ kg Planck's constant h = 6.6 10⁻³⁴ Js The de Broglie wavelength is given by: = h p = h 2mK Squaring both sides and rearranging for kinetic energy K : K = h^2 2m ^2 Substituting the given values: K = (6.6 10⁻³⁴)^2 2 9 10⁻³¹ (5.5 10⁻⁷)^2 K = 43.56 10⁻⁶⁸ 18 10⁻³¹ 30.25 10⁻¹⁴ K = 43.56 10⁻⁶⁸ 544.5 10⁻⁴⁵ K = 0.08 10⁻²³ J K = 8 10⁻²⁵ J Comparing this with x 10⁻²⁵ J, we get x = 8 . Answer: 8