Using the known values for haydrogen atom, calculate
. (a) radius of thirdj orbit for `Li^(+2)`
. (b) speed of electron in fourth orbit for `He^+`
. (c ) angular momentum of electron in 3rd orbit of `He^+.`

Options

A. `O.53 Å` `2.19xx10^6 m//s` `3((h)/(2pi))`
B. `1.59 Å` `2.19xx10^6 m//s` `3((h)/(3pi))`
C. `1.59 Å` `2.19xx10^-6 m//s` `3((h)/(2pi))`
D. `1.59 Å` `2.19xx10^6 m//s` `3((h)/(2pi))`

Answer

D

Explanation

(a) `Z = 3 for Li^+2` . Further we know that `r_n = (n^2)/(Z) a_0`
. Substituting, `n = 3, Z = 3` and `a_0 =0.529Å`
. We have r_3 for `Li^(+2) = ((3)^2/(3)) (0.529)Å`. (b) `Z = 2 for He^+`. Also we know that
. `v_n = (Z)/(n) v_1`
.Substituting,` n = 4, Z=2 and V_1 = 2.19xx10^6 m//s`
. We get, `v_4 for `He^+ = ((2)/(4)) ((2.19xx10^6))m//s`
. `= 1.095xx10^6m//s`. (c ) `L_n = n((h)/(2pi))`
. For `n = 3, L_3 = 3((h)/(2pi))`