Speed of an electron in Bohr's 7ᵗʰ orbit for Hydrogen atom is 3.6 × 10⁶ m / s. The corresponding speed of the electron in 3ʳᵈ orbit, in m / s is :

Solution

Physics sir · 3 steps

In Bohr's model speed goes as 1/n, so the inner orbit is faster by the ratio 7 to 3.

1. Speed in orbit n. In Bohr's model the electron's speed is vₙ = (Z e²)/(2 ε₀ h n). For hydrogen Z = 1, so everything except n is a constant and vₙ ∝ 1/n.

   v₃/v₇ = 7/3

2. Put in numbers. v₃ = 3.6 × 10⁶ × 7/3 = 1.2 × 10⁶ × 7 = 8.4 × 10⁶ m s⁻¹.
3. So. The electron in the 3rd orbit moves at 8.4 × 10⁶ m s⁻¹, which is option (c).

The idea to keep. Bohr speed goes as Z/n: inner orbits are faster. When one orbit's speed is given, take the ratio of n values instead of using the full formula.

Answer from the NTA final answer key. Solution by PrepWiser.