First, you'll need to find the exact model of the Broadcom network adapter chip your notebook has. "802.11n" is just the name of the Wi-Fi standard it supports: Broadcom has several wireless chips supporting that standard.
lspci -nn would be a good command to list all PCI(e) devices on your laptop and their PCI ID numbers: those numbers would allow a more accurate identification.
lsusb will do the same for USB devices.
lspci -nn listing line might look something like this:
12:00.0 Network controller : Broadcom Limited BCM43228 802.11a/b/g/n [14e4:4359]
Here, the numbers [14e4:4359] are the Device ID. The first part specifies the vendor (Broadcom = 14e4) and the second part identifies the device model.
lsusb listing is a bit different, but the Device ID number is similar: 4 hexadecimal digits for the vendor id, a colon, and then 4 hexadecimal digits for the product ID.
You can check here for the Linux support status of various Broadcom chip models: https://wireless.wiki.kernel.org/en/users/drivers/brcm80211
Note that the supported Broadcom chips will need firmware: it is probably available pre-packaged in Ubuntu. If Ubuntu uses the same naming scheme as Debian, the firmware package name should be
With a bit of luck, installing this firmware package and rebooting might be enough to get your Wi-Fi functional if the necessary driver is already in kernel.