How many orbitals in an atom can have the designation 2pz?

There are four quantum numbers for an orbital:

1.  Principal quantum number n: It tells about the position of orbital that is shell number. The values are 1, 2, 3,....

2.  Azimuthal quantum number l: It describes the shape of orbital, for s, p, d, f,... orbitals, the value is 0, 1, 2, 3,... so on.

3. Magnetic quantum number : The value of magnetic quantum number varies from -l to +l (including zero), it defines the sub shell of an orbital.

4. Spin quantum number s: Spin of the electron defines its movement, clockwise or anticlockwise thus, there are only two possible values for spin quantum number that is +1/2 or -1/2.

No two orbitals can have same value for all the four quantum numbers.

orbital is suborbital of 2p orbital, the 2p orbital is drawn in the attachment.

The first three quantum numbers for orbitals are n=2, l=1 and =-1. This set of quantum number is possible for only 1 orbital therefore, there is only 1 orbital with designation .