Question

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

A
two
B
three
C
four
D
one

Solution

## The correct option is B three$$IE=13.6 eV$$Excited photon energy $$12.1 eV$$The energy of the atom at excited state$$=13.6-12.1$$ $$=1.5eV$$$$\therefore {E}_{n}=1.5 eV$$$$E\propto \cfrac{ 1 }{{n}^{2}}$$ $$\Rightarrow {E}_{n}=\cfrac{ JE }{{n}^{2}}$$$$1.5= \cfrac{13.6}{{n}^{2}}$$$${{n}^{2}}=\cfrac{1 3.6}{1.5}=9$$$$n=3$$Physics

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