Bohr Model Energy

Question

A researcher considers a singly ionised helium ion with atomic number two behaving like a hydrogen-like system, and asks for the energy of its ground state in electronvolts.

RankGuru · Accepted Answer

For a hydrogen-like ion with a single electron, NCERT's Bohr analysis gives the energy levels as $E_n=-13.6\,\frac{Z^2}{n^2}$ eV, where $Z$ is the nuclear charge. The energy scales as the square of the atomic number because a larger nuclear charge binds the electron more tightly. Singly ionised helium has $Z=2$, and the ground state has $n=1$, so $E_1=-13.6	imes\frac{4}{1}=-54.4$ eV. The value $-13.6$ eV is wrong because that is hydrogen's ground state with $Z=1$ and ignores the $Z^2$ factor. The value $-27.2$ eV is wrong because it scales linearly with $Z$ rather than as $Z^2$. The value $-6.8$ eV is wrong because it divides rather than multiplies by $Z^2$, loosening the binding instead of tightening it. As stated in NCERT Class 12, Chapter 12 (Atoms), hydrogen-like ions such as He+ and Li2+ follow the same Bohr formula scaled by nuclear charge, since each still has only one electron orbiting a point charge. The stronger nuclear attraction also pulls the orbits inward, shrinking the radius by a factor of $Z$, which is the geometric counterpart of the deeper energy. A magnitude check: doubling the charge quadruples the binding energy, so $-54.4$ eV being exactly four times $-13.6$ eV confirms the $Z^2$ dependence.

Bohr Model Energy

Select the correct option:

🔒 Solution Hidden from View

More atoms and nuclei Practice Questions

A neutron-rich nucleus undergoes beta-minus decay inside a detector, and a student is asked what par...

Following an alpha or beta emission, a daughter nucleus is often left in an excited state and subseq...

In a nuclear reactor, a uranium-235 nucleus captures a slow neutron and splits into lighter fragment...

The Sun generates its enormous power by fusing hydrogen nuclei into helium at its core, and a studen...

A wooden artefact recovered from an excavation shows a carbon-14 activity that is one-fourth of the ...

Given that the mass defect of a helium-4 nucleus is about 0.0304 u, an examiner asks candidates to f...

Looking at the binding-energy-per-nucleon curve, a student notices it peaks near a certain mass numb...

A radioactive sample initially contains 8 billion nuclei of an unstable isotope, and after three suc...

A radioactive isotope used in medical imaging has a half-life of 6 hours, and a technician needs its...

A freshly prepared source contains a large number of identical unstable nuclei, and a researcher obs...

When a heavy parent nucleus undergoes alpha decay, it emits a helium nucleus, and a student must sta...

A chemistry-physics bridge lesson considers the isotope of iron written as iron-56 with atomic numbe...

About This Question

Solution