The more optimal method is to leave 1-3 months worth of expenses as cash and put the rest of the money in something like VTI. You don't want a market crash to erase half of your emergency fund at the exact moment you need it.
Emergency funds should be in FDIC insured savings accounts, that pay at least 50 basis points less than the fed funds rate.
Also, you should have a stash of cash you can find at home in case of power outage or network loss and you can’t get money from the bank. And guns and canned food and clean water.
The optimal method is to invest the $100k in VTI or even a money market fund. You don’t have to leave it as cash.