AIIMS 2019 Physics Bohr's Model MCQ Question

To find the speed of the electron in the fourth orbit of a hydrogen atom (H⁻), we can use the formula for the speed of an electron in a Bohr orbit: $v_n = \frac{Z e^2}{2 \varepsilon_0 h} \cdot \frac{1}{n}$, where $Z$ is the atomic number (1 for H), $e$ is the elementary charge, $\varepsilon_0$ is the permittivity of free space, $h$ is Planck's constant, and $n$ is the principal quantum number (4 for the fourth orbit). Substituting the values yields a speed of approximately $5.45 \times 10^5 \, \text{m/s}$, confirming option B.

Options A and C are incorrect as they provide the same incorrect speed of $5.45 \times 10^6 \, \text{m/s}$, which is too high for the fourth orbit, while option D, $4.45 \times 10^5 \, \text{m/s}$, underestimates the speed based on the same formula. Understanding the relationship between energy levels and electron speeds in atomic orbits is crucial for mastering atomic physics concepts.