The magnetic orbital moment is given by

#mu_"orb" = -g_"L"(e/(2m_e)"L")#

where #"L"# is orbital angular momentum

#|"L"| = sqrt(l(l+1))h/(2pi)#

#g_L# is the electron orbital g- factor which is equal to 1

#l# for a the ground state orbital or **1s** orbital is 0

so the magnetic orbital moment is also **0**

#l# for the 4p orbital is 1

#mu_"orb" = -g_"L"(e/(2m_e)sqrt(l(l+1))h/(2pi))#

#mu_"orb" = -g_"L"(e/(2m_e)sqrt(1(1+1))h/(2pi))#

A unit of magnetic moment called the "Bohr magneton" is introduced here.

#mu_"B" = (ebarh)/(2m_e) ~~ 9.27xx10^24"J/T" #

#barh = h/(2pi)#

# e/(2m_e) = mu_"B"/barh#

#mu_"orb" = -g_"L"(e/(2m_e)sqrt(1(1+1))h/(2pi))#

#=-mu_"B" sqrt(2) #

#-9.27xx10^-24"J/T" xx sqrt(2)#

#~~-9.27xx10^-24"J/T" xx 1.41421356237 #

#-1.310976xx 10 ^-23"J/T"#

So the difference between them is

#1.310976xx 10 ^-23"J/T"#