The radial wave function for 1 s electron in H-atom is `R=(2)/a_(0)^(3//2)e^(-r//a_(0))` where `a_(0)`=radius of `1^(st)` orbit of H-atom . The ratio of probablitiy of `1^(st)` electron in hyrogen atom at distance `a_(0)` from nucleus to that at distance `a_(0)/2` from nucleus.

Options

A. equal
B. `(1)/etime`
C. `(4)/etime`
D. `(e)/4time`

Answer

C

Explanation

probability of finding and electron at a particular distance=`4pi_(2) R^(2)`
`P_(1)=4pir^(2)R^(2)=4pir^(2)xx(4)/(a_(0)^(3))e^(-2r//a_(0))`
`at" "a_(0)" "p_(1)=4pia_(0)^(2)xx(4)/(a_(0)^(3))e^(-2a_(0)//a_(0))`
`at" "a_(0//2)" "p_(2)=4pi(a_(0)^(2))/(4)xx(4)/(a_(0)^(3))e^((-2a_(0))/(2a_(0)))`
`at" "a_(0//2)" "p_(2)/(p_(2))=(4pia_(0)^(2)xx(4)/(a_(0)^(3))e^((-2a_(0))/(2a_(0))))/(4pia_(0)^(2)/(4)xx(4)/(a_(0)^(3))e^((-2a_(0))/(2a_(0))))`
`(p_(1))/(p_(2))=(e^(-))/((1)/(4)e^(-1))=(4)/(e)`