Chemistry

Problem

Consider two hydrogen-like species. In atom A (hydrogen,

Z_1=1

) the electron is in the second orbit (

n_1=2

). In ion B (Li

^{2+}

Z_2=3

) the electron is in the third orbit (

n_2=3

). (i) Derive a general expression for the ratio

v_{1}/v_{2}

of the electron speeds in two hydrogen-like species in terms of their atomic numbers

Z_1

Z_2

and orbit numbers

n_1

n_2

. (ii) Using your expression, determine the numerical value of

v_{1}/v_{2}

for the given atoms A and B. (iii) Which electron is moving faster? Support your answer with calculation.