Energy required to remove an electron from the n=10 state in a hydrogen atom

To determine the energy necessary to remove an electron from the n=10 state in a hydrogen atom, we need to calculate the ionization energy of the atom. The ionization energy is the amount of energy required to completely remove an electron from its atomic shell.

Understanding the energy levels in a hydrogen atom

In a hydrogen atom, electrons occupy discrete energy levels or shells. The energy levels are represented by the principal quantum number (n). The energy of an electron in a hydrogen atom is given by the formula:

E = -13.6/n^2 eV

where E is the energy and n is the principal quantum number. The negative sign indicates that the electron is bound to the nucleus.

Calculating the ionization energy

To remove an electron from the n=10 state, we need to consider the energy difference between this state and the ionized state (where the electron is completely removed).

The energy of the n=10 state is given by:

E(10) = -13.6/10^2 eV

To calculate the ionization energy, we subtract the energy of the ionized state (where n approaches infinity) from the energy of the n=10 state:

Ionization energy = E(infinity) - E(10)
= -13.6/infinity^2 eV - (-13.6/10^2) eV

As the value of n approaches infinity, the energy approaches zero. Therefore, the ionization energy simplifies to:

Ionization energy = 0 eV - (-13.6/10^2) eV
= 13.6/100 eV
= 0.136 eV

Answer

Therefore, the energy necessary to remove the electron from the n=10 state in a hydrogen atom is 0.136 eV. The correct option is (4)0.136 eV.

Option no 4 is correct( formula is - 13.6×z^2÷n^2)..