Q135 / 200 · NEET 2006 · Physics

Ionization potential of hydrogen atom is $13.6 \mathrm{eV}$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 \mathrm{eV}$. According to Bohr's theory, the spectral lines emitted by hydrogen will be:

  • A
    one
  • B
    two
  • Correct answer
    C
    three
  • D
    four

Solution

According to question $$ \begin{aligned} & 12.1=13.6\left(\frac{1}{l^2}-\frac{1}{n^2}\right) \\ & \Rightarrow \quad n^2=\frac{13.6}{1.5}=9 \\ & \Rightarrow \quad n=3 \\ & \end{aligned} $$ Number of spectral lines emitted $$ \begin{aligned} & =\frac{n(n-1)}{2}=\frac{3 \times 2}{2} \\ & =3 \end{aligned} $$

Hence, the correct answer is option: 'C'.

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