Question

Energy of the electron in hydrogen atom in its ground state is 13.6 eV. The energy required (in eV) to move the electron from its ground state to the first excited state, rounded off to TWO decimal places, is .............

Hint:

The energy difference between the ground state and first excited state of a hydrogen atom is 10.2 eV.

Answer 1

Correct Answer: 10 - 10.4

To determine the energy required to move the electron from its ground state to the first excited state in a hydrogen atom, we first need to understand the energy levels of a hydrogen atom. The energy of an electron in the n^th energy level is given by the formula: 
E_n = -13.6 / n² eV.
In the ground state (n = 1), the energy is:
E₁ = -13.6 / 1² = -13.6 eV.
In the first excited state (n = 2), the energy is:
E₂ = -13.6 / 2² = -13.6 / 4 = -3.4 eV.
To find the energy required to move the electron from the ground state to the first excited state, we calculate the difference between these two energy levels:
ΔE = E₂ - E₁ = -3.4 eV - (-13.6 eV) = 10.2 eV.
Thus, the energy required is 10.20 eV.