The value of Rydberg constant $(\mathrm{R}_{\mathrm{H}})$ is $2.18 \times 10^{-18} \mathrm{~J}$. The velocity of electron having mass $9.1 \times 10^{-31} \mathrm{~kg}$ in Bohr's first orbit of hydrogen atom $=\ldots \ldots \ldots \times 10^{5} \mathrm{~ms}^{-1}$ (nearest integer)

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Atomic Structure

The value of Rydberg constant

(R_{H})

2.18 \times 1 0^{- 18} J

. The velocity of electron having mass

9.1 \times 1 0^{- 31} kg

in Bohr's first orbit of hydrogen atom

= \dots\dots\dots \times 1 0^{5} ms^{- 1}

(nearest integer)

Answer: 22

The speed of the electron in the

n

-th Bohr orbit of a hydrogen-like atom is

v = 2.18 \times 1 0^{6} \frac{Z}{n} m s^{- 1}

. For hydrogen's first orbit (

Z = 1, n = 1

v = 2.18 \times 1 0^{6} = 21.8 \times 1 0^{5} \approx 22 \times 1 0^{5} m s^{- 1} .

Hence the answer is 22.

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Integer answer