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CBSE Class 12 Physics 2014 Delhi Set 1 Paper

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Question : 19
Total: 30
A 12.5‌eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy level the hydrogen atoms would be excited? Calculate the wavelength of the first member of Lyman and first member of Balmer series.
Solution:  

For Hydrogen atom
The 1‌st ‌ excited energy =E2−E1=10.2‌eV
The 2‌nd ‌ excited energy =E3−E1=12.09‌eV
The 3‌rd ‌ excited energy =E4−E1=12.75‌eV
Hence, hydrogen atoms will be excited to 4‌th ‌ energy level or 3‌rd ‌ excited state.
For Balmer series
‌
1
λ
‌=R(‌
1
22
−‌
1
32
)
‌
1
λ
‌=R(‌
5
36
)
λ‌=‌
36
5R

λ‌=‌
36
(5×1.09×107)

‌=6.605×10−7m
For Lyman series
‌
1
λ
‌=R(‌
1
12
−‌
1
22
)
‌
1
λ
‌=R(‌
3
4
)
λ‌=‌
4
3R

‌=1.285×10−7m
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