Answer Happy

ans is 0.18 to 0.20
need explanation.
this is gate 2022 question no 59,need correct explanation don't provide incorrect ans or irrelevant ans.
The state of the electron in a He ion is described by the following normaliz wavefunction, (r, 0.0) = 3 7 R₂1 (r)Y₁0(0,0) - i R10 (r) Yoo (8,4) + XR32 (r)Y₂0(80, 4). 8 16 Here, Rnt and Yim represent the radial and angular components of the eigenfunctions of He ion, respectively, and x is an unknown constant. If the energy of the ion is measured in the above state, the probability (rounded off to two decimal places) of obtaining the energy of atomic unit is -
GATE 2022 CHEMISTRY (CY) Q.59 The state of the electron in a He ion is described by the following normalized wavefunction, Y(r, 0.0) = R21 (r)Y₁0(0,0) - ( -Ria(r) Yo R10 (r) Yoo (9.) +xR32 (r)Y₂0 (8. p). Here, Rn and Ym represent the radial and angular components of the eigenfunctions of He ion, respectively, and x is an unknown constant. If the energy of the ion is measured in the above state, the probability (rounded off to two decimal places) of obtaining the energy of atomic unit is www