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CBSE Class 12-science Answered

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Asked by albiinfanta | 14 Mar, 2020, 08:11: PM
answered-by-expert Expert Answer
Energy level En of hydrogen like atom for orbital quantum number n is given by
 
begin mathsize 14px style E subscript n equals space minus space fraction numerator z squared cross times 13.6 over denominator n squared end fraction space e V end style .......................(1)
First line of Lyman series in hydrogen is due to transition from n=2 to n=1
Hence energy difference for first line of Lyman seriesis in hydrogen atom given by
begin mathsize 14px style E subscript L space equals space minus 13.6 space open square brackets 1 over 2 squared space minus space 1 over 1 squared close square brackets space equals space 3 over 4 space cross times 13.6 space e V end style  .................. (2)
Second line of Balmer series in hydrogen-like atom  is due to transition from n=4 to n=2
Hence energy difference for second line of Balmer series in hydrogen-like atom is given by
begin mathsize 14px style E subscript B space equals space minus 13.6 space z squared open square brackets 1 over 4 squared space minus space 1 over 2 squared close square brackets space equals space 3 over 16 space z squared cross times 13.6 space e V end style ..................(3)
By equating equations (2) and (3), we get z = 2
Answered by Thiyagarajan K | 15 Mar, 2020, 09:22: AM
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