'NO' the energy of atomic orbitals depends upon principal as well as azimuthal quantum number, which is more common known as (n+l) rule .
According to (n+l) rule the atomic orbital has less (n+l) value also has less energy vice versa.
For 2S => n= 2, l=0,. =>n+l= 2+0=2
For 2p => n= 2, l=2,. =>n+l= 2+1=3
Hence 2p have more energy than 2s orbital
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