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Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is (14) 1/3 . Find (a) atomic number of the nucleus. (b) the frequency of K α line of the X-ray produced. (R = 1.1 x 10 7 m -1 and c = 3 x 10 8 m/s)

Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is  (14)1/3 . Find (a) atomic number of the nucleus. (b) the frequency of Kα line of the X-ray produced. (R = 1.1 x 107 m-1 and c = 3 x 108 m/s) 

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 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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