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In a hypothetical hydrogen-like atom, the electron is replaced by a negatively charged particle of mass 5m_e (where m_e is the mass of an electron). The angular momentum of this particle in a particular Bohr orbit is given as 3h . If a₀ and E₀ are the radius of the first Bohr orbit and the ground state energy of a normal hydrogen atom respectively, what are the radius and energy of the particle in this specific orbit

Options

  1. A36 a₀, E₀ 36
  2. B1.2 a₀, 5 E₀ 6
  3. C7.2 a₀, 5 E₀ 36
  4. D7.2 a₀, 36 E₀ 5

Correct answer

C. 7.2 a₀, 5 E₀ 36

Step-by-step solution

According to Bohr's quantization condition, the angular momentum L in the n^ th orbit is given by L = nh 2 . Given L = 3h , we have nh 2 = 3h n = 6 . The radius of the n^ th Bohr orbit is inversely proportional to the mass of the orbiting particle and directly proportional to n^2 ( r n^2 m ). For the normal hydrogen atom, r₁ = a₀ . For the hypothetical atom, r₆ = a₀ 6^2 5 = 36 5 a₀ = 7.2 a₀ . The energy of the n^ th Bohr orbit is directly proportional to the mass of the orbiting particle and inversely proportional

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