Question

velocity of electron in 3rd shell of Li+2is (c=velocity of light)
1. 1/137 c

2.1/274 c

3.2/137c​

Answer 1

Answer:

For 3rd shell of Li, Z = 3 & n = 3

# Solution -

Speed of electron in nth orbit of atom is given by -

v = Ze² / 2εnh

Substitute values,

v = 3 × (1.6×10^-19)^2 / (2 × 8.85×10^-12 × 3 × 6.6×10^-34)

v = 2.19×10^6 m/s

Speed of this electron with speed of light will be -

v/c = 2.19×10^6 / 3×10^8

v/c = 0.0073

v = 0.0073 c

v = 1/137 c

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Answer 2

Explanation:

Radius of orbit, rn = n2Z × 0.529 ×10−8 cm

When n=3 and Z=3

r3 =3^2/3×0.529 ×10−8  = 1.587 ×10−8 cm

Now, v=nh/2πmr=

3×6.624×10−272×3.14×9.108×10−28×1.587×10−8= 2.1911 ×108 cm/sec

And velocity of light,c= 3×1010 cm/sec

So, in terms of c velocity of electron can be written as =2.1911×1083×1010=0.7303×10−2 c or 0.7303100c=7303106c