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I was thinking of a homebrew magic weapon to give one of my players, and wanted to see if anyone that it would be unbalanced or broken. It is a longsword that is black and white, split down the middle. If they hit with the dark edge, it would deal an extra 1d6 necrotic damage. If they hit with the white edge, it'd deal an extra 1d6 radiant damage. They would have to specify before rolling their attack roll, which side they would use.

I was thinking this would be an uncommon rarity weapon because it deals half as much damage as a flame tongue, but it could be bumped up to rare because of the two damage types. I would have the player find this by defeating a boss somewhere between 5th and 7th level, depending on the players.

Is something like this unbalanced?

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Being able to switch between two damage types is a nice feature, but it doesn't have a severe impact on gameplay. If we look at this table, we can see that against radiant damage, there are barely any creatures with resistance or immunities, and those are probably good-aligned celestials you're never gonna fight unless you're playing an evil campaign. Vulnerabilities are also pretty much non-existant - in particular against radiant and necrotic - so there's no real advantage gained from that either.

So, conclusion 1: Being able to switch the damage type is certainly a balanced ability that is not too strong.

So, let's compare the damage of 1d6 radiant or necrotic that the weapon deals. Looking at the Treasure section in the DM guide, we can find several weapons with similar damage values:

Frost Brand (p. 171), very rare: deals 1d6 cold, gives resistance to cold, sheds light in a 20ft radius, can extinguish nonmagical flames in a radius 1/day.

Sun Blade (p. 205), rare: finesse longsword that deals radiant instead of slashing damage; +2 to damage and attack rolls; +1d8 against undead; sheds sunlight in a radius (which is useful against vampires, drow or similar creatures)

Flame Tongue (p. 170), rare: bonus action to activate "fire mode", +2d6 damage on hit, sheds light.

So, if we compare 1d6 radiant or necrotic damage bonus to the values above, we could certainly make this weapon an uncommon or rare weapon.

Therefore, conclusion 2: Having a sword deal an extra 1d6 damage is within the realms of a balanced weapon. Depending on versatility and additional effects, a rarity of uncommon or rare would be appropriate.

Hence, taking the "Magic Item Rarity" table in the DMG, p. 135, into account (uncommon: PC lvl1+, rare: PC lvl5+), I would suggest something along the following lines, as opposed to just dealing extra damage:

Blade of Glistening Darkness, rare (requires attunement):
During your turn, you can use a bonus action to evoke one of the following effects, which lasts until you decide to end it (no action required) or until you spend one round without attacking. You also gain a +1 bonus to attack and damage rolls made with this weapon.
Effects:
• Shadows start wreathing around the blade. While this effect is active, you have advantage on intimidation checks against any creature that is not undead. When you hit with an attack, you deal an extra 1d6 necrotic damage.
• The sword emits bright light within 5 feet of you and dim light for another 5 feet. This light counts as sunlight. When you hit with an attack, you deal an extra 1d6 radiant damage.

uncommon version:

Blade of fickle Alignment, uncommon (requires attunement):
While attuned to this weapon, you can switch it from its necrotic to its radiant state and vice versa. During the short rest you use to attune yourself to the weapon, you have to decide on the initial state for the weapon.
When you hit with an attack made with this weapon, you can choose to deal an additional 1d6 damage of the weapon's current type.

Optionally, you can disable one of the respective effects for lawful good and chaotic evil characters, if you want to.

Anyhow, that's just my thoughts on the topic. You're the DM after all, though, so it's up to you to decide, we can only give you advice.

Addition due to OP's suggestion about the weapon "leveling up" as you do good deeds:

You could also use one of the "templates" above and as the wielder performs good deeds, the weapon gains "charges" - one maximum charge initially, and then an increasing maximum of charges the more good deeds are done ("good deeds" as defined by the DM). Those charges would be separate for each wielder. You can expend charges to deal an additional 1d6 damage per charge of the current type on a hit (you decide once you know if you hit). You regain charges on a long rest.
Such a weapon would definitely be rare or very rare, depending on which template you apply it to.
Feel free to change the size of the additional damage die, I'm not sure which value would be perfectly balanced. You could also scale the die with good deeds.

Example charge table:

Max charges | Regained after long rest
1 | 1 (i.e. all)
2 | roll 1d6, divide by 3, round up.
3 | roll 1d6, divide by 2, round up.
4 | roll 1d4

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    \$\begingroup\$ I very much like the idea of having some alignment based effect on it. The more good deeds you do, the brighter the blade gets maybe to the point of 2d6 radiant and vice versa. I think I may steal the Blade of Glistening Darkness, the name is great! Thanks for the answer :) \$\endgroup\$ – bubbajake00 Jan 22 '18 at 22:50
  • \$\begingroup\$ Feel free to use the name (and the rest of the description) as you please, that's what I wrote it for ^^ (that also goes for anyone else who wants to use this in their campaign, obviously) \$\endgroup\$ – PixelMaster Jan 22 '18 at 22:58
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    \$\begingroup\$ @bubbajake00 I made an addition to my answer to account for "good deed" scaling. Depending on which template you apply this to, the rarity might become very rare. If you apply my suggestion to the - currently - rare weapon, you could also use 1d8 or 1d10 for the bonus damage. You should test this with your players, and make sure that they are aware that this die might change later, so they know up front and won't be disappointed if you have to nerf it because it's too strong. \$\endgroup\$ – PixelMaster Jan 22 '18 at 23:19
  • \$\begingroup\$ I like that idea, do enough bad as a good guy and your weapon suffers a bit. Unless of course you do enough bad, then it goes back up lol \$\endgroup\$ – bubbajake00 Jan 23 '18 at 16:22
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    \$\begingroup\$ @bubbajake00 Mind you, it might be more logical to separate good and bad deeds - it makes no sense roleplaywise for the necrotic aspect to become stronger if you help people. Of course, that will get super-complicated super quick, so you're probably better off not using my suggestion. Instead, you could just increase the radiant damage to 2d6 for good-aligned creatures and the necrotic damage to 2d6 for evil-aligned creatures. Neutral creatures could get 1d4 to both radiant and necrotic damage. \$\endgroup\$ – PixelMaster Jan 23 '18 at 16:45

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