why Thinkpad L420 uses 32bit?

If you have more than 4GB, the Ubuntu installer should have installed the PAE kernel, which allows you to use up to 64GB of memory.

If you have put more memory after installation, you can enable the PAE kernel following the instructions:

https://help.ubuntu.com/community/EnablingPAE

Please run 'uname -a' and paste the output here. Thanks!

This status is more appropriate

sorry for the late reply

I put the memory before installation. My laptop was preinstalled with 7-64 bit, and now I want to change it with ubuntu.
I tried to install with 64-bit version and it stucked. Ubuntu recommended L420 with ubuntu 11.10 32-bit version which is limit my memory usage only 4GB.

how do I know if PAE is already enabled?

here is the result of uname
chypa@chypa-L420:~$ uname -a
Linux chypa-L420 3.0.0-17-generic #30-Ubuntu SMP Thu Mar 8 17:34:21 UTC 2012 i686 i686 i386 GNU/Linux

I tried with /proc/cpuinfo
processor : 0
vendor_id : GenuineIntel
cpu family : 6
model : 42
model name : Intel(R) Core(TM) i5-2520M CPU @ 2.50GHz
stepping : 7
cpu MHz : 800.000
cache size : 3072 KB
physical id : 0
siblings : 4
core id : 0
cpu cores : 2
apicid : 0
initial apicid : 0
fdiv_bug : no
hlt_bug : no
f00f_bug : no
coma_bug : no
fpu : yes
fpu_exception : yes
cpuid level : 13
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe nx rdtscp lm constant_tsc arch_perfmon pebs bts xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat epb xsaveopt pln pts dts tpr_shadow vnmi flexpriority ept vpid
bogomips : 4989.14
clflush size : 64
cache_alignment : 64
address sizes : 36 bits physical, 48 bits virtual
power management:

processor : 1
vendor_id : GenuineIntel
cpu family : 6
model : 42
model name : Intel(R) Core(TM) i5-2520M CPU @ 2.50GHz
stepping : 7
cpu MHz : 800.000
cache size : 3072 KB
physical id : 0
siblings : 4
core id : 1
cpu cores : 2
apicid : 2
initial apicid : 2
fdiv_bug : no
hlt_bug : no
f00f_bug : no
coma_bug : no
fpu : yes
fpu_exception : yes
cpuid level : 13
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe nx rdtscp lm constant_tsc arch_perfmon pebs bts xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat epb xsaveopt pln pts dts tpr_shadow vnmi flexpriority ept vpid
bogomips : 4988.44
clflush size : 64
cache_alignment : 64
address sizes : 36 bits physical, 48 bits virtual
power management:

processor : 2
vendor_id : GenuineIntel
cpu family : 6
model : 42
model name : Intel(R) Core(TM) i5-2520M CPU @ 2.50GHz
stepping : 7
cpu MHz : 800.000
cache size : 3072 KB
physical id : 0
siblings : 4
core id : 0
cpu cores : 2
apicid : 1
initial apicid : 1
fdiv_bug : no
hlt_bug : no
f00f_bug : no
coma_bug : no
fpu : yes
fpu_exception : yes
cpuid level : 13
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe nx rdtscp lm constant_tsc arch_perfmon pebs bts xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat epb xsaveopt pln pts dts tpr_shadow vnmi flexpriority ept vpid
bogomips : 4988.43
clflush size : 64
cache_alignment : 64
address sizes : 36 bits physical, 48 bits virtual
power management:

processor : 3
vendor_id : GenuineIntel
cpu family : 6
model : 42
model name : Intel(R) Core(TM) i5-2520M CPU @ 2.50GHz
stepping : 7
cpu MHz : 800.000
cache size : 3072 KB
physical id : 0
siblings : 4
core id : 1
cpu cores : 2
apicid : 3
initial apicid : 3
fdiv_bug : no
hlt_bug : no
f00f_bug : no
coma_bug : no
fpu : yes
fpu_exception : yes
cpuid level : 13
wp : yes
flags : fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe nx rdtscp lm constant_tsc arch_perfmon pebs bts xtopology nonstop_tsc aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 x2apic popcnt aes xsave avx lahf_lm ida arat epb xsaveopt pln pts dts tpr_shadow vnmi flexpriority ept vpid
bogomips : 4988.44
clflush size : 64
cache_alignment : 64
address sizes : 36 bits physical, 48 bits virtual
power management:

/proc/meminfo
MemTotal: 3204516 kB
MemFree: 1088768 kB
Buffers: 700796 kB
Cached: 703872 kB
SwapCached: 0 kB
Active: 1135896 kB
Inactive: 872568 kB
Active(anon): 709780 kB
Inactive(anon): 144340 kB
Active(file): 426116 kB
Inactive(file): 728228 kB
Unevictable: 0 kB
Mlocked: 0 kB
HighTotal: 2345864 kB
HighFree: 1020820 kB
LowTotal: 858652 kB
LowFree: 67948 kB
SwapTotal: 8224764 kB
SwapFree: 8224764 kB
Dirty: 64 kB
Writeback: 0 kB
AnonPages: 603672 kB
Mapped: 106716 kB
Shmem: 250324 kB
Slab: 46508 kB
SReclaimable: 28212 kB
SUnreclaim: 18296 kB
KernelStack: 3200 kB
PageTables: 7852 kB
NFS_Unstable: 0 kB
Bounce: 0 kB
WritebackTmp: 0 kB
CommitLimit: 9827020 kB
Committed_AS: 3050452 kB
VmallocTotal: 122880 kB
VmallocUsed: 42716 kB
VmallocChunk: 74184 kB
HardwareCorrupted: 0 kB
AnonHugePages: 0 kB
HugePages_Total: 0
HugePages_Free: 0
HugePages_Rsvd: 0
HugePages_Surp: 0
Hugepagesize: 4096 kB
DirectMap4k: 16376 kB
DirectMap4M: 892928 kB

Any help will be appreciated.
thanks

3.0.0-17-generic should be 3.0.0-17-generic-pae. Your CPU should definitely support it. Look at the wiki page ara mentioned to see how to install it. I'm surprised it was not installed by the installer in the first place. Did you fit the new RAM after installing Ubuntu or before?

Seems you already answered the question. I can only suggest to try enabling PAE then.