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  4. A hydrogen atom in its ground state is irradiated by light of wavelength 970 mathringA. Taking hc / e =1.237 × 10-6 eV m and the ground state energy of hydrogen atom as -13.6 eV, the number of lines present in the emission spectrum is.

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Q. A hydrogen atom in its ground state is irradiated by light of wavelength $970 \,\mathring{A}$. Taking $hc / e =1.237 \times 10^{-6}\, eV m$ and the ground state energy of hydrogen atom as $-13.6\, eV$, the number of lines present in the emission spectrum is.

JEE AdvancedJEE Advanced 2016

Solution:

$Z=1 $
$n=1 $
$\lambda=970 $
$E=\frac{12400 \,eV }{970}=12.75 \,eV$
Energy difference between $n =1 \& n =4$
So electron transit to $n =4$
$\therefore $ no. of lines in emission spectrum
$=\frac{n(n-1)}{2}=\frac{4(4-1)}{2}=6$