what is the Dimension of Pressure Gradiant and Rydberg constant?

Answer 1

Pressure Gradient :

It is P/L (Pressure / Length)
It's SI units are Pa / m (Pascal / meter)
It's dimensions are M L^(-2) T^ (-2)
Pronounced as "M L power -2 T power -2"

Rydberg Constant :

It is R
It's SI units are m^ (-1) {Meter inverse}
It's dimensions are M^ (0) L^(-1) T^ (0)
Pronounced as "M power 0 L power -1 T power 0"

Where
M is Mass
L is Length
T is Time and
I is Ampere. You can also denote it with A

Hope you understood this.

Answer 2

By dimension I presume you mean units

so pressure is kg /m /s^2 so pressure gradient is
kg /m^2 /s^2

Rydberg constant has dimension of reciprocal length (specifically cm-1)