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1.

Energy levels `A, B, C` of a certain atom corresponding to increasing values of energy i.e., `E_(A) lt E_(B) lt E_(C)`. If `lambda_(1), lambda_(2), lambda_(3)` are the wavelengths of radiations correspnding to the transitions `C` to `B, B` to `A` and `C` to `A` respectively, which o fthe following statements is correct? A. `lambda_(3)=lambda_(1)+lambda_(2)`B. `lambda_(3) =(lambda_(1)lambda_(2))/(lambda_(1)+lambda_(2))`C. `lambda_(1)+lambda_(2)+lambda_(3)=0`D. `lambda_(3)^(2)=lambda_(1)^(2)+lambda_(2)^(2)`

Answer» Correct Answer - B
`(hc)/(lamda_(1))+(hc)/(lamda_(2))=(hc)/(lamda_(3)) implies (lamda_(1)+lamda_(2))/(lamda_(1) lamda_(2))=(1)/(lamda_(3))`
`lamda_(3)=(lamda_(1)lamda_(2))/(lamda_(1)+lamda_(2))`
Discussion
2.

Hydrogen `(H)`, deuterium `(D)`, singly ionized helium `(He^(+))` and doubly ionized lithium `(Li)` all have one electron around the nucleus. Consider `n = 2` to `n = 1` transition. The wavelength of emitted radiations are `lambda_(1), lambda_(2), lambda_(3)` and `lambda_(4)` respectively. then approximatelyA. `lambda_(1)=lambda_(2)=4 lambda_(3)=9 lambda_(4)`B. `4lambda_(1)=2lambda_(2)=2lambda_(3)=lambda_(4)`C. `lambda_(1)=2lambda_(2)=2sqrt(2)lambda_(3)=3sqrt(2)lambda_(4)`D. `lambda_(1)=lambda_(2)=2lambda_(3)=3sqrt(2)lambda_(4)`

Answer» Correct Answer - A
`(1)/(lamda) prop Z^(2) implies lamda prop (1)/(Z^(2))`
`lamda_(1) : lamda_(2) : lamda_(3) :lamda_(4)=(1)/(1^(2)) :(1)/(1^(2)) :(1)/(2^(2)) : (1)/(3^(2))=1: 1:(1)/(4):(1)/(9)`
`lamda_(1)=lamda_(2)=4 lamda_(3)=9lamda_(4)`
Discussion
3.

Electrons in a certain energy level `n=n_(1)` can emit 3 spectral lines. When they are in another energy level, `n=n_(2)`, they can emit 6 spectral lines. The orbital speed of the electrons in the two orbits are in the ratioA. `4 :3 `B. `3:4`C. `2:1`D. `1:2`

Answer» Correct Answer - A
Number of lines in emission spectrum
`(n_(1)(n_(1)-1))/(2)=3 implies n_(1)=3`
`(n_(2)(n_(2)-1))/(2)=6 implies n_(2) =4`
`v_(n) prop (1)/(n)`
`(v_(1))/(v_(2))=((n_(2))/(n_(1)))=(4)/(3)`
Discussion
4.

Let `v_(1)` be the frequency of series limit of Lyman series, `v_(2)` the frequency of the first line of Lyman series and `v_(3)` the frequency of series limit of Balmer series. Then which of the following is correct ?A. `upsilon_(1)-upsilon_(2)=upsilon_(3)`B. `upsilon_(1)=upsilon_(2)-upsilon_(3)`C. `(1)/(upsilon_(2))=(1)/(upsilon_(1))+(1)/(upsilon_(3))`D. `(1)/(upsilon_(1))=(1)/(upsilon_(2))+(1)/(upsilon_(3))`

Answer» Correct Answer - A
`(1)/(c//v_(1))=R((1)/(1^(2))-(1)/(oo))=R`
`(1)/(c//v_(2))=R((1)/(1^(2))-(1)/(2^(2)))=(3R)/(4)`
`(1)/(c//v_(3))=R((1)/(2^(2))-(1)/(oo))=(R )/(4)`
(i)-(ii)=(iii)
`upsilon_(1)-upsilon_(2)=upsilon_(3)`
Discussion
5.

The size of an atom is of the order ofA. `10^(-8) m`B. `10^(-10) m`C. `10^(-12)m`D. `10^(-14)m`

Answer» Correct Answer - B
Discussion