Home › UP Board Class 12 › Atomic Structure › For a hydrogen-like ion of atomic number $Z$, th…
For a hydrogen-like ion of atomic number $Z$, the ground-state energy is:
A$-13.6 Z^2\,\text{eV}$
B$-13.6\,\text{eV}$
C$-13.6 Z\,\text{eV}$
D$-13.6 / Z^2\,\text{eV}$
Answer & Solution
Correct answer: A. $-13.6 Z^2\,\text{eV}$
For a hydrogen-like single-electron ion of charge $+Ze$, $E_n = -13.6\,Z^2/n^2\,\text{eV}$. The ground state has $n = 1$ so $E_1 = -13.6 Z^2\,\text{eV}$. For example $\mathrm{He}^+$ ($Z = 2$) has a ground state energy of $-54.4\,\text{eV}$.
Related questions
Atomic radius is conveniently measured in which unit?Which element has three shells with 8 electrons in its outermost shell?Which sub-particle was discovered LAST?If an element has the configuration 2, 8, 8, 1, its valency and likely group are:Why does the atomic mass of chlorine (35.5) lie between two integers?An atom of oxygen has Z = 8 and A = 16. Number of neutrons is:Why are protons and neutrons together called nucleons?Isotopes of hydrogen include: