Question

What is the angular velocity of an electron occupying second orbit of li2+ ion?

Answer 1

Dear Student,

According to Bohr model,mv2r=KZe2r2or, r=KZe2mv2 ......... ⎛⎝1⎞⎠and also we know that angular momentum of the orbiting electron is quantized, i.e., mvr=nh2π .......... ⎛⎝2⎞⎠from ⎛⎝1⎞⎠ and ⎛⎝2⎞⎠,nh2πmv=KZe2mv2v=2πKZe2nh ....... ⎛⎝2⎞⎠Also, v=rωwhere, ω=angular velocityω=vrω=2πKZe2nhKZe2mv2ω=2πKZe2nh×mv2KZe2or, ω=2πKZe2nh×m(2πKZe2nh)2KZe2ω=2πKZe2nh×m×4π2K2Z2e4n2h2×KZe2ω=m×8π3K2Z2e4n3h3For Li2+, n=2 and Z=3Therefore, ω=9π3mK2e4h3

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