I am planning to install Vmware Vpshere on DELL Embedded PC3000 hardware which is having Intel® Atom Processor E3845 (Quad Core, 2M Cache, 1.91 GHz, 10W), 8GB RAM and 256 SSD storage. Do you see possibility to install the Vmware Vpshere Esxi host on this hardware and then host Linux virtual machine on it.
Check here for system compatibility: VMware Compatibility Guide - System Search
You can also access CPU and IO device checkers from the menu on the page:
Atom processor is an entry consumer level processor whereas vSphere ESXi is a Enterprise level product.
Are you using server hardware or PC hardware?
This might cause some issues with NICs and HBA's
You might be able to make it work like a charm, but it won't be supported by VMware, so you should not run any production workload on that server.