\({\rho _E}\,\, = \,\,\frac{1}{2}\,\,{\varepsilon _0}{E_{r.m.s}}^2\,\, \)\(= \,\,\frac{1}{2}\,\,{\varepsilon _0}\,\,{\left( {\frac{{{E_0}}}{{\sqrt 2 }}} \right)^2} = \,\,\frac{1}{4}\,\,{\varepsilon _0}{E_0}^2\,\,\)\( = \,\,\frac{1}{4}\,\, \times \,\,8.85\,\, \times \,\,{10^{ - 12}}\,\, \times \,\,{\left( 1 \right)^2}\,\, \)\(= \,\,2.2\,\, \times \,\,{10^{ - 12}}\,\,J\,\,{m^{ - 3}}\)