What peaks in their mass spectra could be used to distinguish between 4-methyl-2-pentanone and 2-methyl-3-pentanone?

You can use the peaks at m/z = 15, 29, 71, and 85 to distinguish between the two compounds.

The major fragmentation peaks come from cleavage of the C-C bonds adjacent to the carbonyl group.

4-Methyl-2-pentanone

The structure is

So (CH₃)₂CHCH₂COCH₃ should fragment as

(CH₃)₂CHCH₂-COCH₃ → C₄H₉ + C₂H₃O. This gives m/z = 57 and 43.

(CH₃)₂CHCH₂CO-CH₃ → C₅H₉O + CH₃. This gives m/z = 85 and 15.

The major peaks should be at m/z = 15, 43, 57, and 85.

2-Methyl-3-pentanone

The structure is

So (CH₃)₂CHCOCH₂CH₃ should fragment as

(CH₃)₂CH-COCH₂CH₃→ C₃H₇ + C₃H₅O. This gives m/z = 43 and 57.

(CH₃)₂CHCO-CH₂CH₃ → C₄H₇O + C₂H₅. This gives m/z = 71 and 29.

The major peaks should be at m/z = 29, 43, 57, and 71.

Differences

The peaks at 43 and 57 are common to both.

The first compound should have a major peak at 85 and a small one at 15.

The second compound should have a major peak at 71 and a small one at 29.

Note: This ignores other fragmentation and rearrangement patterns.

For example, the first compound can generate a major peak at 58 by the McLafferty rearrangement.