Sugiro que você edite seu arquivo para:
auto lo
iface lo inet loopback
auto wlp3s0
iface wlp3s0 inet static
address 192.168.0.100
netmask 255.255.255.0
gateway 192.168.0.1
dns-nameservers 192.168.0.1 8.8.8.8
wpa-ssid *****
wpa-psk ******
Teste:
sudo ifdown wlp3s0 && sudo ifup wlp3s0
ping -c3 www.ubuntu.com
Poste quaisquer erros.