(a) Speed of the electron in Bohr’s nth orbit is
v =

e2

2nhε0

= α

c

n

Speed of the electron in Bohr’s first (n = 1) orbit is
v1 =

1

137

×

3×108

1

= 2.186 × 10ms−1 = 2.186 × 106ms−1
v2 =

v1

2

= 1.093 × 106ms−1
v3 =

v1

3

= 0.729 × 106ms−1
(b) Orbital period of electron in Bohr’s first orbit is
T1 =

2πr1

v1

=

2×3.14×0.53×10−10

2.186×10

s = 1.52 × 10−16 s
As Tn = n3T1
∴ T2 = (2)3 × 1.52 × 10–16 = 12.16 × 10–16 = 1.22 × 10–15 s
T3 = (3)3 × 1.52 × 10–16 = 41.04 × 10–16 = 4.10 × 10–15 s.