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"#
