Consider that an electron is revolving in an excited state of Hydrogen atom with velocity √25.6 × 10⁵ ms⁻¹. The radius of the orbit is x × 10⁻⁹ m. The value of x is : [Take the mass of electron to be

Question

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity √25.6 × 10⁵ ms⁻¹. The radius of the orbit is x × 10⁻⁹ m. The value of x is : [Take the mass of electron to be 9 × 10⁻³¹ kg, charge of electron = −1.6 × 10⁻¹⁹ C and 1/4πɛ₀ = 9 × 10⁹ N m² C⁻²]

Accepted Answer

Answer: 1 — mv²/r = (1/4πɛ₀)e²/r² (9 × 10⁻³¹ × 25.6 × 10⁵ × 10⁵)/r = (9 × 10⁹ × 1.6 × 10⁻¹⁹ × 1.6 × 10⁻¹⁹)/r² r = (256 × 10⁻⁴⁰)/(256 × 10⁴ × 10⁵) × (10⁹/10⁻³¹) r = 1 × 10⁻⁹ m = x × 10⁻⁹ m x = 1

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