Modern Physics 4 Question 33

34. If the wavelength of the nth  line of Lyman series is equal to the de-Broglie wavelength of electron in initial orbit of a hydrogen like element (Z=11). Find the value of n.

(2005)

Show Answer

Solution:

  1. nth line of Lymen series means transition from (n+1)th  state to first state.

1λ=RZ211(n+1)2

de-Broglie wavelength in (n+1)th  orbit :

λ=hmv=hrmvr=(2π)(hr)(n+1)h=2πr(n+1) or 1λ=(n+1)2πr

Equating Eqs. (i) and (ii), we get

n+12πr=RZ2n(n+2)(n+1)2

Now, as

rn2Z

r=(n+1)211ro

Substituting in Eq. (iii), we get

112πro=R(11)2(n)(n+2)(n+1) or (n+1)=(1.09×107)(11)(2π)×(0.529×1010)(n2+2n)

Solving this equation,

We get,

n=24



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक