Atoms & Nuclei

JEE Main level, numerical answer, medium

117 of 239

Question 117 of 239

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is x×1015Hzx\times {10}^{15}Hz. The value of x is ________
(Given h=4.25×10−15eVsh=4.25\times {10}^{-15}eVs)

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Answer: 3

Let the higher state be nn.
The number of wavelengths emitted is given by,
n(n−1)2=6⇒n2−n−12=0⇒(n−4)(n+3)=0⇒n=4\dfrac{n(n-1)}{2}=6 \Rightarrow {n}^{2}-n-12=0 \Rightarrow \left(n-4\right)(n+3)=0 \Rightarrow n=4
For hydrogen atom,
hν=13.6(11−116)=(13.6×1516)eVh\nu =13.6\left(\dfrac{1}{1}-\dfrac{1}{16}\right)=\left(13.6\times \dfrac{15}{16}\right)eV⇒ν=Eh=13.6×15×1.6×10−1916×6.62×10−34=3×1015Hz\Rightarrow \nu =\dfrac{E}{h} =\dfrac{13.6\times 15\times 1.6\times {10}^{-19}}{16\times 6.62\times {10}^{-34}} =3\times {10}^{15}Hz

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