In the molecule which you have mentioned here, replacement of any one of the H with different functional group leads to the diastereomeric products since already one prochiral center exist. Therefore, those two protons are diastereotopic.
You can't distinguish enantiomers by NMR. In the case of two prochiral protons, many times these are distinguishable. In this case, I would say they are diastereotopic.
The molecule is achiral because there is a reflection plane perpendicular to the plane of the drawing through the central carbon. The paired hydrogens at positions 1 are diastereotopic with respect to each other because they cannot be interchanged with one another by any symmetry operation. However, each hydrogen at 1 is enantiotopic with respect to the mirror image hydrogen at position 3. It would be easier to see with a Fisher projection.
Be aware of hydrogen bonding in this molecule! The molecule is symmetric with respect to how you have drawn it. Therefore, the hydrogens, as Dr. Kluger said, are diastereotopic with respect to each other. The spectroscopy of this molecule won't be straight forward because of hydrogen bonding, both intermolecular and intramolecular.
I can only add to you reply "...each hydrogen at 1 is enantiotopic with respect to the mirror image hydrogen at position 3..." that each hydrogen at 1 is diastereotopic with respect to hydrogen in position 3' (ie, the hydrogen atom at the other methylene group which is not the mirror image to hydrogen 1).
Drs Kluger and Khlebnikov have given the definitive answers. I might just add an intuitive way of showing that the two hydrogens in each CH2 group are diastereotopic. If you hold the molecule in the conformation you have shown, the R group must be either out toward you or away from you. (It doesn't matter which, because you can turn it on the vertical axis.) Then one member of each CH2 group points toward the R group and one points away. They are clearly diastereotopic with each other and enantiotopic with their mirror twins. As Dr. Kluger said, this becomes apparent in the Fischer projection. This is an interesting example, because the CHR carbon is not a chiral center (nor any kind of stereocenter), yet it renders the CH2 groups diastereotopic in the same way that a chiral center would!
i agree with Thangavelu Saravanan, because in this case, if we change any proton with Deuterium D for example, we will obtain 2 diastereoisomers. so in this case, this proton is called as " diastereotopic " and not " enantiotopic ".
Msahel - when we talk about equivalent, enantiotopic or diastereotopic relations between atoms (or groups), we need to specify which particular atoms or groups we consider. In the molecule which we are discussing in this thread, there are pairs where protons are equivalent, enantiotopic and diastereotopic !
Khlebnikov, here i am talking about changing one proton of one carbone. in this case we will obtain only diastereotopics. in other cases, of course we talk about equivalent, enantiotopic or diastereotopic protons.