I installed a 64-bit OS in a 32-bit processor

As the title suggest, I accidentally installed 64-bit Ubuntu 13.04 in a 32-bit processor, and it is working fine for now (actually I feel my PC became more responsive). Will there be any problem in the near future though? I think my Motherboard is a 64-bit but I'm not certain, but my processor is a 32-bit. Further, I did lscpu and I got this:

Architecture:          x86_64
CPU op-mode(s):        32-bit, 64-bit
Byte Order:            Little Endian
CPU(s):                1
On-line CPU(s) list:   0
Thread(s) per core:    1
Core(s) per socket:    1
Socket(s):             1
NUMA node(s):          1
Vendor ID:             GenuineIntel
CPU family:            15
Model:                 4
Stepping:              9
CPU MHz:               2659.023
BogoMIPS:              5318.04
L1d cache:             16K
L2 cache:              1024K
NUMA node0 CPU(s):     0

If you installed a 64-bit OS your CPU is necessarily 64-bit capable. In a 32-bit only processor the 64-bit installer not even starts.

In lscpu output CPU op-mode(s):32-bit, 64-bit means your CPU is both 32-bit and 64-bit capable. Architecture: x86_64 is the current kernel architecture (64-bit).

You can also check 64-bit support running:

grep " lm " /proc/cpuinfo

If it outputs nothing you have a 32-bit CPU. If it outputs something like flags : blah blah lm blah blah blah your CPU supports Long Mode (AKA 64-bit).

From your output it is clear that you have a 64bit CPU. The line CPU op-mode(s):32-bit, 64-bit means that you have a 64bit CPU.

Therefore there is no problem using a 64bit OS.

Looks like you experienced the same surprise I did a few years ago.

I accidentally put a 64-bit Ubuntu CD in my laptop and installed it, and a bit later I realised "Wait a moment.... I thought my laptop was a 32-bit system?"

If the 64-bit version works on your system, then that means your system is actually a 64-bit system, rather than a 32-bit one as you used to think ;)

Your processor is actually 64-bit processor as this line states:

Architecture: x86_64

If it has been 32-bit, you couldn't have installed a 64-bit OS in the first place. Don't worry, your PC will work just fine.