Question

# According to Bohr's theory of Hydrogen atom, for the electron in the ${n}^{th}$ allowed orbit the kinetic energy is proportional to $\frac{1}{{n}^{2}}$. (True / False)

A
True
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B
False
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Solution

## The correct option is A TrueBohr's model of Hydrogen atom is based on three postulates:Electrons move around the nucleus in circular orbits.The angular momentum of an electron moving in an orbit is quantized.When an electron jumps from on orbit to another, its energy changes and a photon is emitted or absorbed.Kinetic energy of an electron in the Hydrogen atom:By the Bohr's model, the energy of an electron is given by the expression $E=-13.6\frac{{Z}^{2}}{{n}^{2}}eV$, where $Z$ is the ratio of charge of nucleus and proton and is $n$ the number of orbit in which electron is present.So, the energy is inversely proportional to the square of the number of orbit, $KE\propto \frac{1}{{n}^{2}}$.Therefore, it is true.

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