Question

# Choose the correct option for the below-given statements.Statement I: In Bohr’s model, the velocity of electrons increases with a decrease in the positive charge of the nucleus as electrons are not held tightly.Statement II: Velocity decreases with an increase in principal quantum number.

A

Statement I is correct & Statement II is correct

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B

Statement I is correct & Statement II is incorrect

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C

Statement I is incorrect & Statement II is incorrect

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D

Statement I is incorrect & Statement II is correct

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Solution

## The correct option is D Statement I is incorrect & Statement II is correctBohr's law describe the structure of atoms especially that of hydrogen atom proposed by the Danish physics Neil's Bohr in $1913$. The Bohr model is one of the classical model to describe the velocity and radius of electron for hydrogen and hydrogen like species in quantum mechanical description.Statement I:The velocity of the electron, according to Bohr's lawWhere, ${\mathrm{V}}_{\mathrm{o}}=2.18×{10}^{6}×\left(\mathrm{Z}/\mathrm{n}\right)\to \left(\mathrm{i}\right)$where, $\mathrm{Z}$ is atomic number corresponds to positive charge of the hydrogen like species $\mathrm{n}$ is principal quantum numberSo, as $\mathrm{Z}$ decreases, ${\mathrm{V}}_{\mathrm{n}}$ also decreasesHence, velocity of the electron increases as the charge positive charge increases.Hence, Statement I is incorrect, Statement II:From equation ($\mathrm{i}$), As the value of $\mathrm{n}$ decreases, velocity will decrease accordingly.Hence, Statement II is correctTherefore, option d is correct

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