I suspect what limits very long distance sniper bullets is not the velocity or energy of the bullet, but accuracy. That said if you can be accurate at any range and are limited by distance, a more massive bullet can travel farther that a less massive bullet of the same shape etc.
Kinetic energy is 1/2 mv2
So assuming you have maximized the velocity you can impart to a bullet of a given size, the more massive you can make it the more kinetic energy it will carry, and the farther it will go / harder it will hit.
I have wondered before why the depleted uranium is popular for antitank rounds. I assumed it was the mass, but there are more massive metals; gold or even osmium or iridium.
It turns out that for tanks, DU has antipersonnel aspects that I did not know about. The fragments entering the tank burn, and then everything in the tank burns too.
Depleted uranium is favored for the penetrator because it is
self-sharpening and flammable. On impact with a hard target,
such as an armored vehicle, the nose of the rod fractures in such a
way that it remains sharp. The impact and subsequent release of
heat energy causes it to ignite. When a DU penetrator reaches the
interior of an armored vehicle, it catches fire, often igniting
ammunition and fuel, killing the crew and possibly causing the vehicle
Not sure that flammability aspect is relevant to a sniper bullet. I am not sure that without the metal on metal impact it would even get hot enough to catch. Maybe if you are shooting robots that would help. But what about the mass? I assumed DU was crazy expensive but no. Per this source, depleted uranium is surprisingly cheap, very hard and easy to fabricate
In elemental form, depleted uranium's density is comparable to gold
and tungsten. It is two-thirds more dense than lead, and more than
twice as dense as steel. If great material weight in a small volume is
needed, depleted uranium is a contender. It is far less expensive than
tungsten and gold. Tungsten markets for $25 to $45 per pound depending
on the form of the metal, and gold ranges from $4,500 to $6,500 per
pound. Depleted uranium costs $5 per pound from old stockpiles. a
Depleted uranium is more energy efficient to fabricate than tungsten.
Depleted uranium has a melting point of approximately 1100o C compared
to tungsten's approximately 3500o C. Depleted uranium's density is
superior to the form of pressed-powder tungsten most often available
on the market. Tungsten has such a high melting temperature that it is
often fabricated instead by cold compaction of powder. The resulting
density of the compacted metal is less than that of depleted uranium.
b Depleted uranium has a high atomic number -- 92. This high number
makes depleted uranium highly opaque to electromagnetic radiation and
a candidate for use as shielding around all radiation generators. c
Depleted uranium can be formed with a tensile strength exceeding
200,000 pounds-per- square inch (psi) which exceeds the tensile
strength of most structural steels. The reinforcing steel used in
Portland cement concrete requires a tensile strength of 60,000 psi.
So mass per $ it looks like DU is competitive with lead (if you can find anyone to sell it to you). Such a bullet could be hard, massive and cheap. Those aspects look good to me for a sniper bullet, especially a lower velocity (close range / quiet) bullet.
Making DU seem cool for a work of fiction would be a little tricky it seems to me. Maybe someone picks up the bullet and says "damn that is heavy!". For a work of fiction, I think it would be cool to have the sniper bullet be made of polycarbonate jacketed gold. Gold is expensive but readily available. The presence of gold fragments in the victim would be puzzling - was he wearing a necklace that was hit? Then they figure out the bullets are made of gold.