An ion consisting of a helium nucleus (charge ) with a single orbiting electron…

CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

An ion consisting of a helium nucleus (charge

+2e

) with a single orbiting electron behaves similarly to hydrogen but with a larger nuclear charge. (a) Generalize the expression for the allowed radii of a one-electron atom from hydrogen (

Z=1

) to an arbitrary nuclear charge

Z

. (b) Use your result from part (a) to obtain the formula for the allowed radii

r_{n,\text{He}^+}

of the singly ionized helium atom (

Z=2

). (c) Calculate the numerical value of the ground-state radius (

n=1

) for He

^+

and compare it to that of hydrogen by computing the ratio

r_{1,\text{He}^+}/r_{1,\text{H}}

. Express the ratio to two significant figures. (d) Based on your findings, discuss qualitatively how the increased nuclear charge affects the spacing between energy levels compared with hydrogen.

Related theory

Atomic Structure
Bohr's atomic model
Structure of Atom
The nuclear atom
Bohr's Model of Atom

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