Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

Let, electron of hydrogen atom at ground state n1=1v1=e2/n14πε0(h/2π)= e2/2ε0h where, e = 1.6 x 10-19C, ε0= 8.85 x 10-12 /NC2/m2, h = 6.62 x 10-34 Jsthen,v1=e2/2ε0h = (1.6 x 10-19)2/ 2x2x8.85 x 10-12 x 6.62 x 10-34 = 1.09 x 106 m/sfor n3 = 3,then,v1=e2/ n32ε0h = (1.6 x 10-19)2/ 3x2x8.85 x 10-12 x 6.62 x 10-34 = 7.27 x 106 m/s (b) Let T1 = orbital period of electron, n1=1Then, Orbital period is related to orbital speedT1 = 2πr1/v1 where, Radius of the orbit (r1) = n12 h2 ε0/πme2Where, e = 1.6 x 10-19C, ε0= 8.85 x 10-12 /NC2/m2, h = 6.62 x 10-34 JsMass of an electron (m) = 9.1 x10-31 KgTherefore,T1 = 2πr1/v1 = 2xπ x (1)2 x (6.62 x 10-34)2 x 8.85 x 10-12/2.18x106x π x 9.1 x10-31 x(1.6 x 10-19)2 = 15.27 x 10-27 = 1.52 x 10-16 sFor level n2=2T2 = 2πr2/v2 = 2xπ x (2)2 x (6.62 x 10-34)2 x 8.85 x 10-12/1.09x106x π x 9.1 x10-31 x(1.6 x 10-19)2 = 1.22 x 10-15 sFor level n3=3T3 = 2πr3/v3 = 2xπ x (3)2 x (6.62 x 10-34)2 x 8.85 x 10-12/7.27x106x π x 9.1 x10-31 x(1.6 x 10-19)2 = 4.12 x 10-15 sHence, the orbit period in each level is 1.527 x 10-16 s, 1.22 x 10-15 s, 4.12 x 10-15 s respectively.