Grade upto college level Modern Physics

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?

Amit Saxena

12 Years agoGrade upto college level

1 Answer

Navjyot Kalra

12 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 1^st 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 1^st 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
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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?

Amit Saxena

1 Answer

Navjyot Kalra

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