1. We need a group 15 element that:

   • can form $d\pi-d\pi$ bonds with transition metals, and
   • forms a hydride which is the strongest base among hydrides of the other group 15 members that also form $d\pi-d\pi$ bonds.

2. Group 15 elements are: $\mathrm{N,\, P,\, As,\, Sb,\, Bi}$

3. For forming $d\pi-d\pi$ bonds with transition metals, the element should have available $d$ orbitals.

   • Nitrogen does not have vacant $d$ orbitals in its valence shell, so it is excluded.
   • The elements that can participate are: $\mathrm{P,\, As,\, Sb,\, Bi}$

4. Their hydrides are: $\mathrm{PH_3,\, AsH_3,\, SbH_3,\, BiH_3}$

5. In group 15, the basic strength of hydrides decreases down the group because the lone pair becomes less available for donation due to increasing size and poorer overlap effects. Hence: $\mathrm{PH_3 > AsH_3 > SbH_3 > BiH_3}$

6. Therefore, among the group 15 elements capable of forming $d\pi-d\pi$ bonds, the element whose hydride is the strongest base is phosphorus.

7. Atomic number of phosphorus is: $Z = 15$

Therefore, the required atomic number is: $\boxed{15}$