A hydrogen-like ion of atomic number possesses only one electron in orbit about the…

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

Problem

A hydrogen-like ion of atomic number

Z

possesses only one electron in orbit about the nucleus. (i) Derive an algebraic expression for the radius

r_n

of the

n

th stationary orbit in terms of fundamental constants, the principal quantum number

n

, and

Z

. (ii) Using the result of part (i), show explicitly that

r_n\propto\dfrac{n^{2}}{Z}

. (iii) Calculate the numerical value of the radius of the second orbit of

\mathrm{He}^+

with the given constants and express it in ångströms.