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An electron is orbiting in 5^{th} Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.

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#### Solution

Ground state energy E_{1} = −13.6 eV

E_{5} = ?

Energy of electron in Bohr’s orbit is inversely proportional to the square of the principal quantum number.

`therefore"E"_5/"E"_1="n"_1^2/"n"_5^2`

`therefore"E"_5/"E"_1=1^2/5^2`

`therefore"E"_5=(-13.6)/25=-0.544"eV"`

The ionization energy = E_{∞} - E_{5} = 0 − (−0.544) = 0.544 eV

Hence, the ionization energy in the 5^{th} orbit is 0.544 eV.

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