A particle is in the normalized state $$\left| \psi \right\rangle $$ which is a superposition of the energy eigen states $$\left| {{E_0} = 10\,eV} \right\rangle $$   and $$\left| {{E_1} = 30\,eV} \right\rangle .$$   The average value of energy of the particle in the state $$\left| \psi \right\rangle $$ is 20 eV. The state $$\left| \psi \right\rangle $$ is given by

A. $$\frac{1}{2}\left| {{E_0} = 10\,eV} \right\rangle + \frac{{\sqrt 3 }}{4}\left| {{E_1} = 30\,eV} \right\rangle $$

B. $$\frac{1}{{\sqrt 3 }}\left| {{E_0} = 10\,eV} \right\rangle + \sqrt {\frac{2}{3}} \left| {{E_1} = 30\,eV} \right\rangle $$

C. $$\frac{1}{2}\left| {{E_0} = 10\,eV} \right\rangle - \frac{{\sqrt 3 }}{4}\left| {{E_1} = 30\,eV} \right\rangle $$

D. $$\frac{1}{{\sqrt 2 }}\left| {{E_0} = 10\,eV} \right\rangle - \frac{1}{{\sqrt 2 }}\left| {{E_1} = 30\,eV} \right\rangle $$

Answer: Option D