The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is: (a) (h²)/(π² m² r³) (b) (h²)/(8π² m² r³) (c) (h²)/(4π² m² r³) (d) (h²)/(4π m² r³)

Answer: (c). Bohr condition for n = 1: mvr = h/2π ⇒ v = (h)/(2π m r). a = v²/r = (h²)/(4π² m² r²) · 1/r So the answer is (c) (h²)/(4π² m² r³).

The acceleration of an electron in the first orbit of the hydrogen… | JEE Main 2017 (9 Apr, Shift 1)

Q109JEE Main 2017 · 9 APR · SHIFT 1Medium

Bohr Model: Orbits, Speed & Angular Momentum

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is:

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Answer: (c)

Bohr condition for $n = 1$ : $mvr = \frac{h}{2\pi} \Rightarrow v = \frac{h}{2\pi m r}$ .
$a = \frac{v^2}{r} = \frac{h^2}{4\pi^2 m^2 r^2} \cdot \frac{1}{r}$
So the answer is (c) $\frac{h^2}{4\pi^2 m^2 r^3}$ .