The value of Rydberg constant is J. The velocity of electron having mass kg in Bohr's first orbit of hydrogen atom = _____ (nearest integer)

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Solution

Q.
The value of Rydberg constant $(R_{H})$ is $2.18 \times 10^{- 18}$ J. The velocity of electron having mass $9.1 \times 10^{- 31}$ kg in Bohr's first orbit of hydrogen atom = _____ $\times 10^{5} m s^{- 1}$ (nearest integer) [2024]

Ans.
(22) Velocity ( $v$ ) of electron in $n^{t h}$ Bohr orbit of a single electron specie with atomic no. Z is given by:

$ν = 2.18 \times 10^{8} \frac{Z}{n} cm / s$

For hydrogen atom, Z = 1 and for first orbit n = 1.

$ν = 2.18 \times 10^{8} \times \frac{1}{1} cm / s = 2.18 \times 10^{6} m / s ≃ 22 \times 10^{5} m / s$

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