Question

Find ratio of T of rotation of electron in 2nd orbit of Li+2 to that of 1st orbit of C+5 .

Answer 1

Angular momentum of the electron is given by

Ln​=2πnh​, where n is the principle quantum

For the ground state, n=1

L1​=2πh​=mv1​r1​

For the first excited state, n=2

L2​=2π2h​=πh​mv2​r2​=2(2πh​)

=2L1​

∴L2​=2L1​

mv2​r2​=2mv1​r1​

v2​r2​=2v1​r1​

w2​r22​=2w1​r12​

w2​=r22​2w1​r12​​, or f2​=r22​2f1​r12​​=r22​T1​2r12​​

Now, the radius of orbit in a hydrogen is given by

r=zr1​n2​=r1​n2

For the first excited state, r2​=r1​(2)2=4r1​

∴r1​r2​​=4

Answer 2

Answer:

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Explanation: