Matter Waves What is the wavelength of an electron moving with a speed of 5.97 * 106m/s? The mass of the electron is 9.11 x 10-31 kg. Consider the following three moving objects: (i) a golf ball with a mass of 45.9 g moving at a speed of 50.0 m/s, (ii) An electron moving at a speed of 3.50 * 105m/s, (iii) A neutron moving at a speed of 2.3 x 102m/s. List the three objects in order from shortest to longest de Broglie wavelength, (a) i< iii< ii (b) ii< iii< i (c) iii< ii< i (d) i< ii< iii (e) iii< i< ii

Solution: Here, we are going to arrange the given three objects in order from shortest to longest de Broglie wavelength. Step1: According to de-Broglie, the wavelength associated with a particle of mass m, moving with velocity v is given by, --------(1) Where, = wavelength of the particle -34 H = Planck’s constant and its value is 6.626 x 10 J.s v = velocity of the particle Step2: i) For the golf ball with a mass of 45.9 g moving at a speed of 50.0 m/s, m = 45.9 g = 0.0459 Kg v = 50.0 m/sec Substituting the values in equation (1), we get, = (6.626 x 10 -34J.s) / (0.0459 Kg X 50.0 m/sec) -34 = 2.89 x 10 m Thus, wavelength of the golf ball = 2.89 x 10 -34m 5 ii) For the electron moving at a speed of 3.50 x 10 m/s, m = 9.1 x 10 -31Kg 5 v = 3.50 x 10 m/s Substituting the values in equation (1), we get, -34 -31 5 = (6.626 x 10 J.s) / [(9.1 x10 Kg) X (3.50 x 10 m/s)] = 0.208 x 10 m-8 -9 = 2.08 x 10 m Thus, wavelength of the electron = 2.08 x 10 m. -9 2 iii) For the neutron moving at a speed of 2.3 x 10 m/s, m = 1.67 x 10 -27Kg 2 v = 2.3 x 10 m/s Substituting the values in equation (1), we get, -34 -27 2 = (6.626 x 10 J.s) / [(1.67 x10 Kg) X (2.3 x 10 m/s)] = 1.725 x 10 m-9 Thus, wavelength of the neutron = 1.725 x 10 m. -9 Step3: The increasing order of de-Broglie wavelength is: Golf ball < neutron < electron Thus, the correct option is (a). --------------------- .