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in Physics by (25 points)
A hydrogen atom is in ground state. Then to get six lines in emission spectrum, wavelength of incident radiation should be [2017]

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1 Answer

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The number of spectral lines emitted, during transition is, n(n-1)/2

=> 6 =n/n(n-1)

=> 12= n2-n

=> n2 -  n -12 =0

=> n2 -  4n -3n-12 =0

=> n(n-4) + 3(n-4) = 0

=> (n+3(n-4) = 0

n = -3,4

Considering positive value, we have n=4

Now, \(\frac{1}{\lambda}=R(\frac{1}{1^2}-\frac{1}{4^2})\)

=> \(\lambda\)​ =16/15R= 975​​​​​​ Å

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