Question

The wave function `Phi_(n,l,m_(1))` is a methematical function whose value depends upon shperical upon spherical polar coordinates `(r,theta,phi)` of the electron and characterized by the quantum numbers, n,l and `m_(1)`. Here r is distance from nucleus, `theta` is colatitude and `phi` is azimuth. in the mathematical functions given in the table, Z is atomic number, `a_(0)` is Bohr radius.
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Q. For hydrogen atom the only CORRECT combination is :
A. (I) (iv) (R)
B. (I) (I) (P)
C. (II) (i) (Q)
D. (I) (i) (S)

Answer 1

Correct Answer - D
1s (orbita) has wave function `Phi_("nlm")prop((Z)/(a_(0)))^((3)/(2))E^(-Zr//a_(0))`
`E=-(Z^(2))/(n^(2))xx13.6eV`
`DeltaE_(2-4)=(1)/(16)xx13.6-(-(1)/(4)xx13.6)`
`=(3)/(16)xx13.6eV`
`DeltaE_(2-6)=-(1)/(36)xx13.6-(-(1)/(4)xx13.6)`
`=(8)/(36)xx13.6eV`
`(DeltaE_(2-4))/(DeltaE_(2-6))=(3//16xx13.6eV)/(3//36xx13.6eV)`
`=(3xx36)/(16xx8)=(27)/(32)`
`thereforeDeltaE_(2-4)=(27)/(32)DeltaE_(2-6)`