For a hydrogen-like ion with atomic number (singly-ionised helium, He ):

CHEMISTRY · Subjective · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

For a hydrogen-like ion with atomic number

Z = 2

(singly-ionised helium, He

^{+}

): (a) Write the symbolic expression for the radius

r_n

of the

n

th stationary orbit in terms of the relevant physical constants. (b) Using

n = 3

, calculate: (i) the numerical value of the orbital radius

r_3

, and (ii) the speed

v_3

of the electron in that orbit. Take

h = 6.63\times10^{-34}\,\text{J\,s}

m = 9.11\times10^{-31}\,\text{kg}

e = 1.60\times10^{-19}\,\text{C}

, and

k = 8.99\times10^{9}\,\text{N\,m}^2\text{/C}^2

. Express

r_3

in ångströms (

1\,\text{Å} = 10^{-10}\,\text{m}

) and

v_3

\text{m\,s}^{-1}