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MHT CET202523 Apr 2025Morning ShiftPhysicsAtomic PhysicsActual

In hydrogen atom, the energy of electron in first and third orbit is ' E ₁ ^ and ' E₃ ^ respectively. If E₃=x E₁ then the value of x will be

Options

  1. A1 9
  2. B1 64
  3. C1 27
  4. D1 8

Correct answer

A. 1 9

Step-by-step solution

The energy of an electron in the n^ th orbit of a hydrogen atom is given by E_ n = - 13.6 n² eV . For the ground state ( n=1 ), E₁ = - 13.6 1² = -13.6 eV . For the third orbit ( n=3 ), E₃ = - 13.6 3² = - 13.6 9 eV . Given the relation E₃ = x E₁ , substitute the expressions: - 13.6 9 = x (-13.6) . Divide both sides by -13.6 and simplify: 1 9 = x . The value of x is 1 9 , so the correct option is A.

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