Question

What does the negative electronic energy (negative sign for all values of energy) for hydrogen atom means?

• A. The energy of an electron in the atom is lower than the energy of a free electron at rest which is taken as zero
• B. When the electron is free from the influence of nucleus it has a negative value which becomes more negative
• C. When the electron is attracted by the nucleus the energy is absorbed which means a negative value
• D. Energy is released by hydrogen atom in ground state

Answer 1

Answer: (A)

The energy of an electron in the atom is lower than the energy of a free electron at rest which is taken as zero

Answer 2

The energy of the electron in a hydrogen atom has a negative sign for all possible orbits. This negative sign means that the energy of the electron in the atom is lower than the energy of a free electron at rest. A free electron at rest means that is infinitely far away from the nucleus and has the negligible attraction towards the nucleus. Thus it is assigned the energy value of zero. Mathematically, this corresponds to setting the orbit 'n' equal to infinity in the energy equation, such that $E _{\infty}=0$. As the electron gets closer to the nucleus (as n decreases), $E _{ n }$ becomes larger in absolute value and more and more negative. The most negative energy value is given by $n=1$ which corresponds to the most stable orbit. It is called the ground state of an atom.