A beam of electrons is incident on a single slit that has awidth of 1.00 × 10 –

Question

A beam of electrons is incident on a single slit that has awidth of 1.00 × 10–6 m and adiffraction pattern is observed on a screen located 15.0 m from theslit. The momentum of an individual electron in the beam is 5.91× 10–24 kg•m/s. What is thewidth of the central maximum fringe?

b. 5.87 ×10–5 m
c. 3.37 ×10–3 m
d. 6.67 ×10–4 m
e. 7.50 × 10–3 m A beam of electrons is incident on a single slit that has awidth of 1.00 × 10–6 m and adiffraction pattern is observed on a screen located 15.0 m from theslit. The momentum of an individual electron in the beam is 5.91× 10–24 kg•m/s. What is thewidth of the central maximum fringe? 5.87 ×10–5 m 3.37 ×10–3 m 6.67 ×10–4 m 7.50 × 10–3 m

Explanation / Answer

According to De broglie's theory we have = (h/m * v) = (h/p) ---------(1) h is planck's constant and has a value 6.63 * 10-34J-s p is the momentum of an individual electron and is equal to5.91 * 10–24 kg•m/s substituting the above values in equation (1) we get thewavelength of the electron beam the width of the central maximum fringe ybright = L * (m * /d) L = 15.0 m m = 1 and d =  1.00 *10–6 m

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