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# Atomic Structure - 7

Q.3. Wave function of 2s electron is given by . It has node at r = r_{0}. Find relation b/w r_{0} & a_{0}.

Ans:

^{2}_{25} = 0 at r = r_{0}

[__Dumb Question__: Why ^{2}_{25} or prob. of finding electron is zero ?

Ans: At r = r_{0}, it has node where probability of finding electron is zero.]

In this expression, only factor can be zero is

2 - = 0 r_{0} = 2a_{0}

Q.4. A dye absorbs light of = 4530 A^{0} & then fluorescence light of 50870 A^{0}. 47% of absorbed energy is reemitted out as flurescence. Calculate ratio of quanta emitted out to no. of quanta absorbed.

Let n_{1} photons areabsorbed. _{absorbed}

Total energy absorbed =

E of light re-emitted out in one photon =

Let n_{2} photons are reemitted then,

Total energy reemitted out =

As given

E_{absorbed} x = E_{reemitted out}

x = n_{2} x

__ Dumb Question__: What is fluorescence ?

Ans: Emission of radiation from particle ?

Q.5. Waht H-like ion has wavelength difference b/w I

^{st}lines of Balmer & Lyman series equal to 59.3 nm R

_{H}= 109678 cm

^{-1}

Ans: = R

_{H}z

^{2}

For I line of Balmer series

= R

_{H}z

^{2}x R

_{H}x z

^{2}

_{B}=

R

_{H}z

_{L}=

_{B}-

_{L}= 59.3 x 10

^{-7}cm.

= 59.3 x 10

^{-7}

[7.2 - 1.333] = 59.3 x 10

^{-7}

z

^{2}=

z = 3

H-like atom is Li

^{2+}.