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The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:

Question

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly:

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Solution

The Balmer series corresponds to electronic transitions in the hydrogen atom from energy levels n > 2 to n = 2. The ground state of hydrogen corresponds to n = 1.

  1. First, we need to calculate the energy of the hydrogen atom in its ground state (n = 1). The energy of a level n in a hydrogen atom is given by the formula: E_n = -13.6/n^2 eV. So, for n = 1, E_1 = -13.6 eV.

  2. Then, we calculate the energy of the level n = 2, which is the final level in the Balmer series transitions. Using the same formula, for n = 2, E_2 = -13.6/2^2 = -3.4 eV.

  3. The energy required for the transition from n = 1 to n = 2 is the difference in energy between these two levels. So, the energy required is E_2 - E_1 = -3.4 - (-13.6) = 10.2 eV.

Therefore, the minimum energy required by a hydrogen atom in ground state to emit radiation in the Balmer series is nearly 10.2 eV.

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