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In hydrogen – like atom (z = 11), nth line of Lyman series has wavelength λ. The de- Broglie’s wavelength of electron in the level from which it originated is also λ. Find the value of n?

In hydrogen – like atom (z = 11), nth line of Lyman series has wavelength λ. The de- Broglie’s wavelength of electron in the level from which it originated is also λ. Find the value of n?  

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
Hello Student,
Please find the answer to your question
Note : nth line of Lyman series means electron jumping from (n + 1 )th orbit to 1st orbit.
For an electron to revolve in (n + 1)th orbit.
2πr = (n + 1 )λ
⇒ λ = 2π / (n + 1) x r = 2π / (n + 1) [ 0.529 x 10-10] (n + 1)2 / Z
⇒ 1 / λ = Z / 2π [0.529 x 10-10] (n + 1) …(i)
Also we know that when electron jumps from (n + 1)th orbit to 1st orbit
1/ λ = RZ2 [ 1 / 12 – 1 / (n + 1)2 = 1.09 x 107 Z2 [ 1 – 1 / (n + 1)2]
From (i) and (ii)
Z / 2π (0.529 x 10-10) (n + 1) = 1. 09 x 107 Z2 [1 – 1 / (n + 1)2]
On solving, we get n = 24
Thanks
Navjot Kalra
askIITians Faculty

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